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1
Akargun, Yigit Hayri. "Least-squares Finite Element Solution Of Euler Equations With Adaptive Mesh Refinement". Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614138/index.pdf.
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Least-squares finite element method (LSFEM) is employed to simulate 2-D and axisymmetric flows governed by the compressible Euler equations. Least-squares formulation brings many advantages over classical Galerkin finite element methods. For non-self-adjoint systems, LSFEM result in symmetric positive-definite matrices which can be solved efficiently by iterative methods. Additionally, with a unified formulation it can work in all flight regimes from subsonic to supersonic. Another advantage is that, the method does not require artificial viscosity since it is naturally diffusive which also appears as a difficulty for sharply resolving high gradients in the flow field such as shock waves. This problem is dealt by employing adaptive mesh refinement (AMR) on triangular meshes. LSFEM with AMR technique is numerically tested with various flow problems and good agreement with the available data in literature is seen.
2
Amoignon, Olivier. "Numerical Methods for Aerodynamic Shape Optimization". Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-6252.
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Holder, Justin. "Fluid Structure Interaction in Compressible Flows". University of Cincinnati / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ucin159584692691518.
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Tota, Prasad Venkateshwara. "Meshless Euler solver using radial basis functions for solving inviscid compressible flows". [Ames, Iowa : Iowa State University], 2006.
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Cole, Jeffrey William. "Hydrodynamic stability of compressible boundary layer flows". Thesis, University of Exeter, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282650.
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Zuppel, Eddy. "A numerical method for compressible viscous fluid flows /". Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=80158.
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The steady two-dimensional compressible Navier-Stokes equations are solved using an iterative pseudo-time relaxation technique. An implicit first-order accurate Euler scheme is implemented after augmenting the steady governing equations by pseudo-time derivative terms, including artificial compressibility in the continuity equation and preconditioning in the energy equation. These augmented equations are modified by lagging certain flow variables in pseudo-time and by applying approximate factorization and an alternating direction implicit (ADI) method to split the solution procedure into two successive sweeps.Spatial discretization is performed on a stretched staggered grid using central differencing. Then, the momentum equations are decoupled with the elimination of the pressure terms using the continuity equation. The problem is thus reduced to the solution of a series of scalar tridiagonal systems of equations.
The computational method is validated for laminar incompressible flows in channels with downstream-facing steps and for laminar compressible flows past symmetric airfoils.
7
Rudgyard, Michael A. "Cell vertex methods for compressible gas flows". Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.279991.
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Nejat, Amir. "A higher-order accurate unstructured finite volume Newton-Krylov algorithm for inviscid compressible flows". Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/30969.
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A fast implicit (Newton-Krylov) finite volume algorithm is developed for higher-order unstructured
(cell-centered) steady-state computation of inviscid compressible flows (Euler
equations). The matrix-free General Minimal Residual (GMRES) algorithm is used for solving
the linear system arising from implicit discretization of the governing equations, avoiding
expensive and complicated explicit computation of the higher-order Jacobian matrix. An
Incomplete Lower-Upper factorization technique is employed as the preconditioning strategy
and a first-order Jacobian as a preconditioning matrix. The solution process is divided
into two phases: start-up and Newton iterations. In the start-up phase an approximate
solution of the fluid flow is computed which includes most of the physical characteristics
of the steady-state flow. A defect correction procedure is proposed for the start-up phase
consisting of multiple implicit pre-iterations. At the end of the start-up phase (when the
linearization of the flow field is accurate enough for steady-state solution) the solution is
switched to the Newton phase, taking an infinite time step and recovering a semi-quadratic
convergence rate (for most of the cases). A proper limiter implementation for higher-order
discretization is discussed and a new formula for limiting the higher-order terms of the
reconstruction polynomial is introduced. The issue of mesh refinement in accuracy measurement
for unstructured meshes is revisited. A straightforward methodology is applied for
accuracy assessment of the higher-order unstructured approach based on total pressure loss,
drag measurement, and direct solution error calculation. The accuracy, fast convergence
and robustness of the proposed higher-order unstructured Newton-Krylov solver for different
speed regimes are demonstrated via several test cases for the 2nd, 3rd and 4th-order
discretization. Solutions of different orders of accuracy are compared in detail through several
investigations. The possibility of reducing the computational cost required for a given
level of accuracy using high-order discretization is demonstrated.Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate
9
Michalak, Christopher. "Efficient high-order accurate unstructured finite-volume algorithms for viscous and inviscid compressible flows". Thesis, University of British Columbia, 2009. http://hdl.handle.net/2429/7094.
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High-order accurate methods have the potential to dramatically reduce the computational time needed for aerodynamics simulations. This thesis studies the discretization and efficient convergence to steady state of the high-order accurate finite-volume method applied to the simplified problem of inviscid and laminar viscous two-dimensional flow equations. Each of the three manuscript chapters addresses a specific problem or limitation previously experienced with these schemes. The first manuscript addresses the absence of a method to maintain monotonicity of the solution at discontinuities while maintaining high-order accuracy in smooth regions. To resolve this, a slope limiter is carefully developed which meets these requirements while also maintaining the good convergence properties and computational efficiency of the least-squares reconstruction scheme. The second manuscript addresses the relatively poor convergence properties of Newton-GMRES methods applied to high-order accurate schemes. The globalization of the Newton method is improved through the use of an adaptive local timestep and of a line search algorithm. The poor convergence of the linear solver is improved through the efficient assembly of the exact flux Jacobian for use in preconditioning and to eliminate the additional residual evaluations needed by a matrix-free method. The third manuscript extends the discretization method to the viscous fluxes and boundary conditions. The discretization is demonstrated to achieve the expected order of accuracy. The fourth-order scheme is also shown to be more computationally efficient than the second-order scheme at achieving grid-converged values of drag for two-dimensional laminar flow over an airfoil.
10
Slack, David Christopher. "The development of solution algorithms for compressible flows". Diss., This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-07282008-134254/.
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Kolibal, Joseph. "Aspects of finite volume method for compressible flows". Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.237837.
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Tam, Anna. "An anisotropic adaptive method for the solution of 3-D inviscid and viscous compressible flows". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0003/NQ40309.pdf.
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Mossi, Michele. "Simulation of benchmark and industrial unsteady compressible turbulent fluid flows /". [S.l.] : [s.n.], 1999. http://library.epfl.ch/theses/?nr=1958.
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Greaves, Deborah Mary. "Numerical modelling of laminar separated flows and inviscid steep waves using adaptive hierarchical meshes". Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.308788.
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Shelton, Andrew Brian. "A multi-resolution discontinuous galerkin method for unsteady compressible flows". Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24715.
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Thesis (Ph.D.)--Aerospace Engineering, Georgia Institute of Technology, 2009.Committee Chair: Smith, Marilyn; Committee Co-Chair: Zhou, Hao-Min; Committee Member: Dieci, Luca; Committee Member: Menon, Suresh; Committee Member: Ruffin, Stephen
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Kupiainen, Marco. "Compressible Turbulent Flows : LES and Embedded Boundary Methods". Doctoral thesis, KTH, Numerisk analys, NA, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-10090.
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Sermeus, Kurt. "Multi-dimensional upwind discretization and application to compressible flows". Doctoral thesis, Universite Libre de Bruxelles, 2013. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209519.
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This thesis is concerned with the further development and analysis of a class of Computational Fluid Dynamics (CFD) methods for the numerical simulation of compressible flows on unstructured grids, known as Residual Distribution (RD).The RD method constitutes a class of discretization schemes for hyperbolic systems
of conservation laws, which forms an attractive alternative to the more classical Finite Volume methods, particularly since it allows better representation of the flow physics by genuinely multi-dimensional upwinding and offers second-order accuracy on a compact stencil.
Despite clear advantages of RD schemes, they also have some unexpected anomalies in common with Finite Volume methods and an attempt to resolve them is presented. The most notable anomaly is the violation of the entropy condition, which as a consequence allows unphysical expansion shocks to exist in the numerical solution. In the thesis the genuinely multi-dimensional character of this anomaly is analyzed and a multi-dimensional entropy fix is presented and shown to avoid expansion shocks. Another infamous anomaly is the carbuncle phenomenon, an instability observed in many numerical solutions with strong shocks, such as the bow shock on a blunt body in hypersonic flow. The occurence of the carbuncle phenomenon with RD methods is analyzed and a novel formulation for a shock fix, based on an anisotropic diffusion term added in the shock layer, is presented and shown to cure the anomaly in 2D and 3D hypersonic flow problems.
In the present work an effort has been made also to an objective and quantitative assessment of the merits of the RD method for typical aerodynamical engineering applications, such as the transonic flow over airfoils and wings.
Validation examples including inviscid, laminar as well as high Reynolds number turbulent flows
and comparisons against results from state-of-the-art Finite Volume methods are presented.
It is shown that the second-order multi-dimensional upwind RD schemes have an accuracy which is at least as good as second-order FV methods using dimension-by-dimension upwinding and that their main advantage lies in providing excellent monotone shock capturing.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished
18
Ramos, Alejandro. "Development of a Meshless Method to Solve Compressible Potential Flows". DigitalCommons@CalPoly, 2010. https://digitalcommons.calpoly.edu/theses/337.
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The utility of computational fluid dynamics (CFD) for solving problems of engineering interest has experienced rapid growth due to the improvements in both memory capacity and processing speed of computers. While the capability now exists for the solution of the Navier-Stokes equations about complex and complete aircraft configurations, the bottleneck within the process is the time consuming task of properly generating a mesh that can accurately solve the governing partial differential equations (PDEs). This thesis explored two numerical techniques that attempt to circumvent the difficulty associated with the meshing process by solving a simplified form of the continuity equation within a meshless framework. The continuity equation reduces to the full potential equation by assuming irrotational flow. It is a nonlinear PDE that can describe flows for a wide spectrum of Mach numbers that do not exhibit discontinuities. It may not be an adequate model for the detailed analysis of a complex flowfield since viscous effects are not captured by this equation, but it is an appealing alternative for the aircraft designer because it can provide a quick and simple to implement estimate of the aerodynamic characteristics during the conceptual design phase.
The two meshless methods explored in this thesis are the Dual Reciprocity Method (DRM) and the Generalized Finite Difference Method (GFD). The Dual Reciprocity Method was shown to have the capability to solve for the two-dimensional subcritical compressible flow over a Circular Cylinder and the non-lifting flow for a NACA 0012 airfoil. Unfortunately these solutions were obtained with the requirement of a priori knowledge of the solution to tune a parameter necessary for proper convergence of the algorithm. Due to the shortcomings of applying the Dual Reciprocity Method, the Generalized Finite Difference Method was also investigated. The GFD method solves a PDE in differential form and can be thought of as a meshless form of a standard finite difference scheme. This method proved to be an accurate and general technique for solving the previously mentioned cases along with the lifting flow about a NACA 0012 airfoil. It was also demonstrated that the GFD method could be formulated to discretize the full potential equation with second order accuracy. Both solution methods offer their own set of unique advantages and challenges, but it was determined that the GFD Method possessed the flexibility necessary for a meshless technique to become a viable aerodynamic design tool.
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D'Angelo, Stefano. "Adjoint-based error estimation for adaptive Petrov-Galerkin finite element methods: Application to the Euler equations for inviscid compressible flows". Doctoral thesis, Universite Libre de Bruxelles, 2015. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/228297.
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The current work concerns the study and the implementation of a modern algorithm for a posteriori error estimation in Computational Fluid Dynamics (CFD) simulations based on partial differential equations (PDEs). The estimate involves the use of duality argument and proper consistent discretisation of primal and dual problem.A key element is the construction of the adjoint form of the primal differential operators where the data term is a quantity of interest depending on the application. In engineering, this is typically a physical functional of the solution. So, by solving this adjoint problem, it is possible to obtain important information about local sensitivity of the error with respect to the current target quantity and thereby, we are able to perform an a posteriori error representation based on adjoint data. Through this, we provide local error indicators which can drive an adaptive meshing algorithm in order to optimally reduce the target error. Therefore, we first derive and solve the discrete primal problem in agreementwith the chosen numerical method. According to consistency and compatibility conditions, we can use the same discretisation for solving the adjoint problem, simply by swapping the position of the unknowns and the test functions in the linearised variational operator. Remembering that the corresponding adjoint problem always remains linear, the computational cost for obtaining these data is limited compared to the effort needed to solve the primal nonlinear problem.This procedure, fully developed for Discontinuous Galerkin (DG) and Finite Volume (FV) methods, is here for the first time applied in a fully consistent way for Petrov-Galerkin (PG) discretisations. Differently from the latter, the biggest issue for the PG method becomes the need to handle two different functional spaces in the discretisation, one of which is often not even continuous. Stabilized finite element schemes such as Streamline Upwind (SUPG), bubble stabilized (BUBBLE) Petrov-Galerkin and stabilized Residual Distribution (RD) have been selected for implementation and testing. Indeed, based on local advection information, these schemes are naturally more suitable for solving hyperbolic problems and therefore, interesting alternatives for fluid dynamics applications.A scalar linear advection equation is used as a model problem for convergence rate of both primal and adjoint solutions and target quantity. In addition, it is also applied in order to verify the accuracy of the adjoint-based a posteriori error estimate. Next, we apply the methods to a complete collection of numerical examples, starting from scalar Burgers’ problem till 2D compressible Euler equations. Through suited quantities of interest, we illustrate aspects of the adjoint mesh refinement by comparing its efficiency with respect to the standard a posteriori error estimation.Doctorat en Sciences de l'ingénieur et technologie
info:eu-repo/semantics/nonPublished
20
Lucas, Daniel. "A highly adaptive three dimensional hybrid vortex method for inviscid flows and helically symmetric vortex equilibria". Thesis, University of St Andrews, 2012. http://hdl.handle.net/10023/3091.
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This thesis is concerned with three-dimensional vortex dynamics, in particular the modelling of vortex structures in an inviscid context. We are motivated by the open problem of regularity of the inviscid equations, i.e. whether or not these equations possess solutions. This problem is manifest in small scales, where vortex filaments are stretched and intensify as they are drawn into increasingly thin tendrils. This creates great difficulty in the investigation of such flows. Our only means of experimentation is to perform numerical simulations, which require exceptionally high resolution to capture the small scale vortex structures. A new numerical method to solve the inviscid Euler equations for three-dimensional, incompressible fluids is presented, with special emphasis on spatial adaptivity to resolve as broad a range of scales as possible in a completely self-similar fashion. We present a hybrid vortex method whereby we discretise the vorticity in Lagrangian filaments and perform and inversion to compute velocity on an arbitrary unstructured finite-volume grid. This allows for a two-fold adaptivity strategy. First, although naturally spatially adaptive by definition, the vorticity filaments undergo ‘renoding'. We redistribute nodes along the filament to concentrate their density in regions of high curvature. Secondly the Eulerian mesh is adapted to follow high strain by increasing resolution based on local filament dimensions. These features allow vortex stretching and folding to be resolved in a completely automatic and self-similar way. The method is validated via well known vortex rings and newly discovered helical vortex equilibria are also used to test the method. We begin by presenting this new class of three-dimensional vortex equilibria which possess helical symmetry. Such vortices are observed in propeller and wind turbine wakes, and their equilibria shapes have until now been unknown. These vortices are described by contours bounding regions of uniform axial vorticity. Material conservation of axial vorticity enables equilibria to be calculated simply by a restriction on the helical stream function. The states are parameterised by their mean radius and centroid position. In the case of a single vortex, the parameter space cannot be fully filled by our numerical approach. We conjecture that multiply connected contours will characterise equilibria where the algorithm fails. We also consider multiple vortices, evenly azimuthally spaced about the origin. In such cases instabilities often lead to a single helical vortex.
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Hariharan, Nathan. "High order simulation of unsteady compressible flows over interacting bodies with overset grids". Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/12960.
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Sorensen, K. A. "A multigrid accelerated procedure for the solution of compressible fluid flows on unstructured hybrid meshes". Thesis, Swansea University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.639089.
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A method for solving compressible fluid flow problems is described. The convergence of the solver is accelerated with the use of a multigrid scheme where the coarse meshes are created in an automatic way, using grid agglomeration. For viscous flows, a methodology for the application of unstructured hybrid meshes is proposed. A geometrically conservative, second order scheme for flows involving geometry movement for these meshes is presented. The performance of the method is illustrated in several examples of inviscid and viscous, steady-state and time-dependent flow. The complexity of the geometries considered spans from two-dimensional aerofoils to complex aircraft configurations.
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Crittenden, Thomas M. "Fluid actuators for high speed flow control". Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/7742.
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In order to extend fluid-based flow control techniques that have been demonstrated at low subsonic speeds to high speed flows, it is necessary to develop actuators having sufficient momentum to control and manipulate high speed flows. Two fluidic actuation approaches are developed where the control jet may reach supersonic velocities and their performance is characterized. The first actuator is a compressible synthetic (zero net mass flux) jet. This is an extension of previous work on synthetic jets with an increase in driver power yielding substantial pressurization of the cavity such that the flow is compressible. The jet is generated using a piston/cylinder actuator, and the effects of variation of the orifice diameter, actuation frequency, and compression ratio are investigated. Operation in the compressible regime uniquely affects the time-dependent cylinder pressure in that the duty cycle of the system shifts such that the suction phase is longer than the blowing phase. The structure of the jet in the near-field is documented using particle image velocimetry and Schlieren flow visualization. In the range investigated, the stroke length is sufficiently long that the jet flow is dominated by a starting jet rather than a starting vortex (which is typical of low-speed synthetic jets). A simple, quasi-static numerical model of the cylinder pressure is developed and is in generally good agreement with the experimental results. This model is used to assess system parameters which could not be measured directly (e.g., the dynamic gas temperature and mass within the cylinder) and for predictions of the actuator performance beyond the current experimental range. Finally, an experiment is described with self-actuated valves mounted into the cylinder head which effectively icrease the orifice area in suction and overcome some of the limitations inherent to compressible operation.
The second actuation concept is the combustion-driven jet actuator. This device consists of a small-scale (nominally 1 cc) combustion chamber which is filled with premixed fuel and oxidizer. The mixture is ignited using an integrated spark gap, creating a momentary high pressure burst within the combustor that drives a high-speed jet from an exhaust orifice. At these scales, the entire combustion process is complete within several milliseconds and the cycle resumes when fresh fuel/oxidizer is fed into the chamber and displaces the remaining combustion products. The actuator performance is characterized by using dynamaic measurements of the combustor pressure along with Schlieren flow visualization, limited dynamic thrust measurements, and flame photography. The effects of variation in the following system parameters are investigated: fuel type and mixture ratio, exhaust orifice diameter, chamber aspect ratio, chamber volume, fuel/air flow rate, ignition/combustion frequency, and spark ignition energy. The resulting performance trends are documented and the basis for each discussed. Finally, a proof-of-concept experiment demonstrates the utility of teh combustion-driven jet actuators at low-speed for transitory reattachment of a separated flow over an airfoil at high angles of attack.
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Padioleau, Thomas. "Development of "all-régime" AMR simulation methods for fluid dynamics, application in astrophysics and two-phase flows". Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASP086.
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Bien que performantes pour la capture des chocs, la plupart des méthodes de simulation standards ne sont pas adaptées à des régimes de Mach variés. Des méthodes numériques innovantes, utilisant des schémas de type Volumes Finis, robustes et précises uniformément selon le nombre de Mach (dites "tout régime") ont été récemment élaborées au CEA. Ces méthodes permettent de résoudre les équations de la mécanique des fluides compressibles pour capturer des chocs, mais aussi pour simuler des écoulements à très faible vitesse. Fort de ces résultats prometteurs, nous proposons dans cette thèse de mettre à l’épreuve ces nouvelles méthodes dans deux domaines applicatifs différents: les écoulements diphasiques à petit échelle et les écoulements compressibles en astrophysique. Pour ces deux domaines la simulation multi-régime est un point difficile. En effet, ces deux contextes d’applications ont pour cœur une modélisation d’écoulement compressible mais mettent en jeu des phénomènes de convection et de compressibilité à des régimes de Mach très variés. L’approche "tout régime" permettra de capturer des phénomènes très compressibles tout en gardant la précision sur les écoulements basse vitesseAlthough classic simulation methods for compressible flow are efficient for shock capturing, they are not adapted to variable Mach regimes. Innovative methods using Finite Volume numerical schemes, robust and uniformly accurate with respect to the Mach number (so-called "all-regime"), were recently developed at CEA. These methods allow to solve the equations of compressible flows for both shocks capturing and flows involving very low material speed. Using the ground of these promising results, we propose within this thesis to challenge these new methods in two different application areas: small scale two-phase flows and compressible flows in astrophysics. For both contexts the multi-regime simulation is a key issue: they both rely on a compressible flow modeling but involve convection and compressibility in highly-variable Mach regimes. The "all-regime" approach is a good candidate for capturing highly compressible phenomena while preserving the accuracy in the low speed flows
25
Strodtbeck, Joshua. "A FILTER-FORCING TURBULENCE MODEL FOR LARGE EDDY SIMULATION INCORPORATING THE COMPRESSIBLE "POOR MAN'S" NAVIER--STOKES EQUATIONS". UKnowledge, 2012. http://uknowledge.uky.edu/me_etds/13.
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A new approach to large-eddy simulation (LES) based on the use of explicit spatial filtering combined with backscatter forcing is presented. The forcing uses a discrete dynamical system (DDS) called the compressible ``poor man's'' Navier--Stokes (CPMNS) equations. This DDS is derived from the governing equations and is shown to exhibit good spectral and dynamical properties for use in a turbulence model. An overview and critique of existing turbulence theory and turbulence models is given. A comprehensive theoretical case is presented arguing that traditional LES equations contain unresolved scales in terms generally thought to be resolved, and that this can only be solved with explicit filtering. The CPMNS equations are then incorporated into a simple forcing in the OVERFLOW compressible flow code, and tests are done on homogeneous, isotropic, decaying turbulence, a Mach 3 compression ramp, and a Mach 0.8 open cavity. The numerical results validate the general filter-forcing approach, although they also reveal inadequacies in OVERFLOW and that the current approach is likely too simple to be universally applicable. Two new proposals for constructing better forcing models are presented at the end of the work.
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Bailey, David A. "A ghost fluid, finite volume continuous rezone/remap Eulerian method for time-dependent compressible Euler flows". Thesis, University of Reading, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.414620.
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Choudhary, Aniruddha. "Verification of Compressible and Incompressible Computational Fluid Dynamics Codes and Residual-based Mesh Adaptation". Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/51169.
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Code verification is the process of ensuring, to the degree possible, that there are no algorithm deficiencies and coding mistakes (bugs) in a scientific computing simulation. In this work, techniques are presented for performing code verification of boundary conditions commonly used in compressible and incompressible Computational Fluid Dynamics (CFD) codes. Using a compressible CFD code, this study assesses the subsonic inflow (isentropic and fixed-mass), subsonic outflow, supersonic outflow, no-slip wall (adiabatic and isothermal), and inviscid slip-wall. The use of simplified curved surfaces is proposed for easier generation of manufactured solutions during the verification of certain boundary conditions involving many constraints. To perform rigorous code verification, general grids with mixed cell types at the verified boundary are used. A novel approach is introduced to determine manufactured solutions for boundary condition verification when the velocity-field is constrained to be divergence-free during the simulation in an incompressible CFD code. Order of accuracy testing using the Method of Manufactured Solutions (MMS) is employed here for code verification of the major components of an open-source, multiphase flow code - MFIX. The presence of two-phase governing equations and a modified SIMPLE-based algorithm requiring divergence-free flows makes the selection of manufactured solutions more involved than for single-phase, compressible flows. Code verification is performed here on 2D and 3D, uniform and stretched meshes for incompressible, steady and unsteady, single-phase and two-phase flows using the two-fluid model of MFIX.
In a CFD simulation, truncation error (TE) is the difference between the continuous governing equation and its discrete approximation. Since TE can be shown to be the local source term for the discretization error, TE is proposed as the criterion for determining which regions of the computational mesh should be refined/coarsened. For mesh modification, an error equidistribution strategy to perform r-refinement (i.e., mesh node relocation) is employed. This technique is applied to 1D and 2D inviscid flow problems where the exact (i.e.,
analytic) solution is available. For mesh adaptation based upon TE, about an order of magnitude improvement in discretization error levels is observed when compared with the uniform mesh.Ph. D.
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Abbate, Emanuela. "Numerical methods for all-speed flows in fluid-dynamics and non-linear elasticity". Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0409/document.
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Dans cette thèse on s’intéresse à la simulation numérique d’écoulements des matériaux compressibles, voir fluides et solides élastiques. Les matériaux considérés sont décrits avec un modèle monolithique eulérian, fermé avec une loi d’état hyperélastique qui considère les différents comportements des matériaux. On propose un nouveau schéma de relaxation qui résout les écoulements compressibles dans des différents régimes, avec des nombres de Mach très petits jusqu’à l’ordre 1. Le schéma a une formulation générale qui est la même pour tous le matériaux considérés, parce que il ne dépend pas directement de la loi d’état. Il se base sur une discrétisation complétement implicite, facile à implémenter grâce à la linéarité de l’opérateur de transport du système de relaxation. La discrétisation en espace est donnée par la combinaison de flux upwind et centrés, pour retrouver la correcte viscosité numérique dans les différents régimes. L’utilisation de mailles cartésiennes pour les cas 2D s’adapte bien à une parallélisation massive, qui permet de réduire drastiquement le temps de calcul. De plus, le schéma a été adapté pour la résolution sur des mailles quadtree, pour implémenter l’adaptativité de la maille avec des critères entropiques. La dernière partie de la thèse concerne la simulation numérique d’écoulements multi-matériaux. On a proposé une nouvelle méthode d’interface “sharp”, en dérivant les conditions d’équilibre en implicite. L’objectif est la résolution d’interfaces physiques dans des régimes faiblement compressibles et avec un nombre de Mach faible, donc les conditions multi-matériaux sont couplées au schéma implicite de relaxationIn this thesis we are concerned with the numerical simulation of compressible materials flows, including gases, liquids and elastic solids. These materials are described by a monolithic Eulerian model of conservation laws, closed by an hyperelastic state law that includes the different behaviours of the considered materials. A novel implicit relaxation scheme to solve compressible flows at all speeds is proposed, with Mach numbers ranging from very small to the order of unity. The scheme is general and has the same formulation for all the considered materials, since a direct dependence on the state law is avoided via the relaxation. It is based on a fully implicit time discretization, easily implemented thanks to the linearity of the transport operator in the relaxation system. The spatial discretization is obtained by a combination of upwind and centered schemes in order to recover the correct numerical viscosity in different Mach regimes. The scheme is validated with one and two dimensional simulations of fluid flows and of deformations of compressible solids. We exploit the domain discretization through Cartesian grids, allowing for massively parallel computations (HPC) that drastically reduce the computational times on 2D test cases. Moreover, the scheme is adapted to the resolution on adaptive grids based on quadtrees, implementing adaptive mesh refinement techinques. The last part of the thesis is devoted to the numerical simulation of heterogeneous multi-material flows. A novel sharp interface method is proposed, with the derivation of implicit equilibrium conditions. The aim of the implicit framework is the solution of weakly compressible and low Mach flows, thus the proposed multi-material conditions are coupled with the implicit relaxation scheme that is solved in the bulk of the flow
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Durmus, Gokhan. "Parallel Navier Stokes Solutions Of Low Aspect Ratio Rectangular Flat Wings In Compressible Flow". Phd thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/3/12605442/index.pdf.
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The objective of this thesis is to accomplish the three dimensional parallel thin-layer Navier-Stokes solutions for low aspect ratio rectangular flat wings in compressible flow. Two block parallel Navier Stokes solutions of an aspect ratio 1.0 flat plate with sharp edges are obtained at different Mach numbers and angles of attack. Reynolds numbers are of the order of 1.0E5-3.0E5. Two different grid configurations, the coarse and the fine grids, are applied in order to speed up convergence. In coarse grid configuration, 92820 total grid points are used in two blocks, whereas it is 700,000 in fine grid. The flow field is dominated by the vortices and the separated flows. Baldwin Lomax turbulence model is used over the flat plate surface. For the regions dominated by the strong side edge vortices, turbulence model is modified using a polar coordinate system whose origin is at the minimum pressure point of the vortex. In addition, an algebraic wake-type turbulence model is used for the wake region behind the wing. The initial flow variables at the fine grid points are obtained by the interpolation based on the coarse grid results previously obtained for 40000 iterations. Iterations are continued with the fine grid about 20000-40000 more steps. Pressures of the top surface are predicted well with the exception of leading edge region, which may be due to unsuitable turbulence model and/or grid quality. The predictions of the side edge vortices and the size of the leading edge bubble are in good agreement with the experiment.
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Sigfrids, Timmy. "Hot wire and PIV studies of transonic turbulent wall-bounded flows". Licentiate thesis, KTH, Mechanics, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-1577.
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The compressible turbulent boundary layer developing over atwo-dimensional bump which leads to a supersonic pocket with aterminating shock wave has been studied. The measurements havebeen made with hot-wire anemometry and Particle ImageVelocimetry (PIV).
A method to calibrate hot-wire probes in compressible ow hasbeen developed which take into account not only the ow velocitybut also the inuence of the Mach number, stagnation temperatureand uid density. The calibration unit consists of a small jetow facility, where the temperature can be varied. The hot wiresare calibrated in the potential core of the free jet. The jetemanates in a container where the static pressure can becontrolled, and thereby the gas density. The calibration methodwas verfied in the at plate zero pressure gradient turbulentboundary layer in front of the bump at three different Machnumbers, namely 0.3, 0.5 and 0.7. The profiles were alsomeasured at different static pressures in order to see theinuence of varying density. Good agreement between the profilesmeasured at different pressures, as well as with the standardlogarithmic profile was obtained.
The PIV measurements of the boundary layer ow in front ofthe 2D bump showed good agreement with the velocity profilesmeasured with hotwire anemometry. The shock wave boundary layerinteraction was investigated for an inlet Mach number of 0.69.A lambda shock wave was seen on the downstream side of thebump. The velocity on both sides of the shock wave as measuredwith the PIV was in good agreement with theory. The shock wavewas found to cause boundary layer separation, which was seen asa rapid growth of the boundary layer thickness downstream theshock. However, no back ow was seen in the PIV-data, probablybecause the seeding did not give enough particles in theseparated region. The PIV data also showed that the shock wavewas oscillating, i.e. it was moving approximately 5 mm back andforth. This distance corresponds to about five boundary layerthicknesses in terms of the boundary layer upstream theshock.
Descriptors:Fluid mechanics, compressible ow,turbulence, boundary layer, hot-wire anemometry, PIV, shockwave boundary layer interaction, shape factor.
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Sambasivan, Shiv Kumar. "A sharp interface Cartesian grid hydrocode". Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/593.
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Dynamic response of materials to high-speed and high-intensity loading conditions is important in several applications including high-speed flows with droplets, bubbles and particles, and hyper-velocity impact and penetration processes. In such high-pressure physics problems, simulations encounter challenges associated with the treatment of material interfaces, particularly when strong nonlinear waves like shock and detonation waves impinge upon them. To simulate such complicated interfacial dynamics problems, a fixed Cartesian grid approach in conjunction with levelset interface tracking is attractive. In this regard, a sharp interface Cartesian grid-based, Ghost Fluid Method (GFM) is developed for resolving embedded fluid, elasto-plastic solid and rigid (solid) objects in hyper-velocity impact and high-intensity shock loaded environment. The embedded boundaries are tracked and represented by virtue of the level set interface tracking technique. The evolving multi-material interface and the flow are coupled by meticulously enforcing the boundary conditions and jump relations at the interface. In addition, a tree-based Local Mesh Refinement scheme is employed to efficiently resolve the desired physics. The framework developed is generic and is applicable to interfaces separating a wide range of materials and for a broad spectrum of speeds of interaction (O(km/s)). The wide repertoire of problems solved in this work demonstrates the flexibility, stability and robustness of the method in accurately capturing the dynamics of the embedded interface. Shocks interacting with large ensembles of particles are also computed.
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Post, Pascal [Verfasser], Mare Francesca [Gutachter] di i Uwe [Gutachter] Gampe. "Development of efficient numerical methods for non-ideal compressible fluid flows in propulsion and power / Pascal Post ; Gutachter: Francesca di Mare, Uwe Gampe ; Fakultät für Maschinenbau". Bochum : Ruhr-Universität Bochum, 2020. http://d-nb.info/1221370146/34.
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Dobes, Jiri. "Numerical algorithms for the computation of steady and unsteady compressible flow over moving geometries: application to fluid-structure interaction". Doctoral thesis, Universite Libre de Bruxelles, 2007. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210640.
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This work deals with the development of numerical methods for compressible flow simulation with application to the interaction of fluid flows and structural bodies.
First, we develop numerical methods based on multidimensional upwind residual distribution (RD) schemes. Theoretical results for the stability and accuracy of the methods are given. Then, the RD schemes for unsteady problems are extended for computations on moving meshes. As a second approach, cell centered and vertex centered finite volume (FV) schemes are considered. The RD schemes are compared to FV schemes by means of the 1D modified equation and by the comparison of the numerical results for scalar problems and system of Euler equations. We present a number of two and three dimensional steady and unsteady test cases, illustrating properties of the numerical methods. The results are compared with the theoretical solution and experimental data.
In the second part, a numerical method for fluid-structure interaction problems is developed. The problem is divided into three distinct sub-problems: Computational Fluid Dynamics, Computational Solid Mechanics and the problem of fluid mesh movement. The problem of Computational Solid Mechanics is formulated as a system of partial differential equations for an anisotropic elastic continuum and solved by the finite element method. The mesh movement is determined using the pseudo-elastic continuum approach and solved again by the finite element method. The coupling of the problems is achieved by a simple sub-iterative approach. Capabilities of the methods are demonstrated on computations of 2D supersonic panel flutter and 3D transonic flutter of the AGARD 445.6 wing. In the first case, the results are compared with the theoretical solution and the numerical computations given in the references. In the second case the comparison with experimental data is presented.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished
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Sundström, Elias. "Flow instabilities in centrifugal compressors at low mass flow rate". Doctoral thesis, KTH, Mekanik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-217821.
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A centrifugal compressor is a mechanical machine with purpose to convert kineticenergy from a rotating impeller wheel into the fluid medium by compressingit. One application involves supplying boost air pressure to downsized internalcombustion engines (ICE). This allows, for a given combustion chamber volume,more oxygen to the combustion process, which is key for an elevated energeticefficiency and reducing emissions. However, the centrifugal compressor is limitedat off-design operating conditions by the inception of flow instabilities causingrotating stall and/or surge. These instabilities appear at low flow rates andtypically leads to large vibrations and stress levels. Such instabilities affectthe operating life-time of the machine and are associated with significant noiselevels.The flow in centrifugal compressors is complex due to the presence of a widerange of temporal- and spatial-scales and flow instabilities. The success fromconverting basic technology into a working design depends on understandingthe flow instabilities at off-design operating conditions, which limit significantlythe performance of the compressor. Therefore, the thesis aims to elucidate theunderlying flow mechanisms leading to rotating stall and/or surge by means ofnumerical analysis. Such knowledge may allow improved centrifugal compressordesigns enabling them to operate more silent over a broader operating range.Centrifugal compressors may have complex shapes with a rotating partthat generate turbulent flow separation, shear-layers and wakes. These flowfeatures must be assessed if one wants to understand the interactions among theflow structures at different locations within the compressor. For high fidelityprediction of the complex flow field, the Large Eddy Simulation (LES) approachis employed, which enables capturing relevant flow-driven instabilities underoff-design conditions. The LES solution sensitivity to the grid resolution usedand to the time-step employed has been assessed. Available experimentaldata in terms of compressor performance parameters, time-averaged velocity,pressure data (time-averaged and spectra) were used for validation purposes.LES produces a substantial amount of temporal and spatial flow data. Thisnecessitates efficient post-processing and introduction of statistical averagingin order to extract useful information from the instantaneous chaotic data. Inthe thesis, flow mode decomposition techniques and statistical methods, suchas Fourier spectra analysis, Dynamic Mode Decomposition (DMD), ProperOrthogonal Decomposition (POD) and two-point correlations, respectively, areemployed. These methods allow quantifying large coherent flow structures atvfrequencies of interest. Among the main findings a dominant mode was foundassociated with surge, which is categorized as a filling and emptying processof the system as a whole. The computed LES data suggest that it is causedby substantial periodic oscillation of the impeller blade incidence flow angleleading to complete system flow reversal. The rotating stall flow mode occurringprior to surge and co-existing with it, was also captured. It shows rotating flowfeatures upstream of the impeller as well as in the diffuser.QC 20171117
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Ben, Hassan Saïdi Ismaïl. "Numerical simulations of the shock wave-boundary layer interactions". Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS390/document.
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Les situations dans lesquelles une onde de choc interagit avec une couche limite sont nombreuses dans les industries aéronautiques et spatiales. Sous certaines conditions (nombre de Mach élevé, grand angle de choc…), ces interactions entrainent un décollement de la couche limite. Des études antérieures ont montré que la zone de recirculation et le choc réfléchi sont tous deux soumis à un mouvement d'oscillation longitudinale à basse fréquence connu sous le nom d’instabilité de l’interaction onde de choc / couche limite (IOCCL). Ce phénomène appelé soumet les structures à des chargement oscillants à basse fréquence qui peuvent endommager les structures.L’objectif du travail de thèse est de réaliser des simulations instationnaires de l’IOCCL afin de contribuer à une meilleure compréhension de l’instabilité de l’IOCCL et des mécanismes physiques sous-jacents.Pour effectuer cette étude, une approche numérique originale est utilisée. Un schéma « One step » volume fini qui couple l’espace et le temps, repose sur une discrétisation des flux convectifs par le schéma OSMP développé jusqu’à l’ordre 7 en temps et en espace. Les flux visqueux sont discrétisés en utilisant un schéma aux différences finies centré standard. Une contrainte de préservation de la monotonie (MP) est utilisée pour la capture de choc. La validation de cette approche démontre sa capacité à calculer les écoulements turbulents et la grande efficacité de la procédure MP pour capturer les ondes de choc sans dégrader la solution pour un surcoût négligeable. Il est également montré que l’ordre le plus élevé du schéma OSMP testé représente le meilleur compromis précision / temps de calcul. De plus un ordre de discrétisation des flux visqueux supérieur à 2 semble avoir une influence négligeable sur la solution pour les nombres de Reynolds relativement élevés considérés.En simulant un cas d’IOCCL 3D avec une couche limite incidente laminaire, l’influence des structures turbulentes de la couche limite sur l’instabilité de l’IOCCL est supprimée. Dans ce cas, l’unique cause d’IOCCL suspectée est liée à la dynamique de la zone de recirculation. Les résultats montrent que seul le choc de rattachement oscille aux fréquences caractéristiques de la respiration basse fréquence du bulbe de recirculation. Le point de séparation ainsi que le choc réfléchi ont une position fixe. Cela montre que dans cette configuration, l’instabilité de l’IOCCL n’a pas été reproduite.Afin de reproduire l’instabilité de l’IOCCL, la simulation de l’interaction entre une onde de choc et une couche limite turbulente est réalisée. Une méthode de turbulence synthétique (Synthetic Eddy Method - SEM) est développée et utilisée à l’entrée du domaine de calcul pour initier une couche limite turbulente à moindre coût. L’analyse des résultats est effectuée en utilisant notamment la méthode snapshot-POD (Proper Orthogonal Decomposition). Pour cette simulation, l’instabilité de l’IOCCL a été reproduite. Les résultats suggèrent que la dynamique du bulbe de recirculation est dominée par une respiration à moyenne fréquence. Ces cycles successifs de remplissage / vidange de la zone séparée sont irréguliers dans le temps avec une taille maximale du bulbe de recirculation variant d’un cycle à l’autre. Ce comportement du bulbe de recirculation traduit une modulation basse fréquence des amplitudes des oscillations des points de séparation et de recollement et donc une respiration basse fréquence de la zone séparée. Ces résultats suggèrent que l’instabilité de l’IOCCL est liée à cette dynamique basse fréquence du bulbe de recirculation, les oscillations du pied du choc réfléchi étant en phase avec le point de séparationSituations where an incident shock wave impinges upon a boundary layer are common in the aeronautical and spatial industries. Under certain circumstances (High Mach number, large shock angle...), the interaction between an incident shock wave and a boundary layer may create an unsteady separation bubble. This bubble, as well as the subsequent reflected shock wave, are known to oscillate in a low-frequency streamwise motion. This phenomenon, called the unsteadiness of the shock wave boundary layer interaction (SWBLI), subjects structures to oscillating loads that can lead to damages for the solid structure integrity.The aim of the present work is the unsteady numerical simulation of (SWBLI) in order to contribute to a better understanding of the SWBLI unsteadiness and the physical mechanism causing these low frequency oscillations of the interaction zone.To perform this study, an original numerical approach is used. The one step Finite Volume approach relies on the discretization of the convective fluxes of the Navier Stokes equations using the OSMP scheme developed up to the 7-th order both in space and time, the viscous fluxes being discretized using a standard centered Finite-Difference scheme. A Monotonicity-Preserving (MP) constraint is employed as a shock capturing procedure. The validation of this approach demonstrates the correct accuracy of the OSMP scheme to predict turbulent features and the great efficiency of the MP procedure to capture discontinuities without spoiling the solution and with an almost negligible additional cost. It is also shown that the use of the highest order tested of the OSMP scheme is relevant in term of simulation time and accuracy compromise. Moreover, an order of accuracy higher than 2-nd order for approximating the diffusive fluxes seems to have a negligible influence on the solution for such relatively high Reynolds numbers.By simulating the 3D unsteady interaction between a laminar boundary layer and an incident shock wave, we suppress the suspected influence of the large turbulent structures of the boundary layer on the SWBLI unsteadiness, the only remaining suspected cause of unsteadiness being the dynamics of the separation bubble. Results show that only the reattachment point oscillates at low frequencies characteristic of the breathing of the separation bubble. The separation point of the recirculation bubble and the foot of the reflected shock wave have a fixed location along the flat plate with respect to time. It shows that, in this configuration, the SWBLI unsteadiness is not observed.In order to reproduce and analyse the SWBLI unsteadiness, the simulation of a shock wave turbulent boundary layer interaction (SWTBLI) is performed. A Synthetic Eddy Method (SEM), adapted to compressible flows, has been developed and used at the inlet of the simulation domain for initiating the turbulent boundary layer without prohibitive additional computational costs. Analyses of the results are performed using, among others, the snapshot Proper Orthogonal Decomposition (POD) technique. For this simulation, the SWBLI unsteadiness has been observed. Results suggest that the dominant flapping mode of the recirculation bubble occurs at medium frequency. These cycles of successive enlargement and shrinkage of the separated zone are shown to be irregular in time, the maximum size of the recirculation bubble being submitted to discrepancies between successive cycles. This behaviour of the separation bubble is responsible for a low frequency temporal modulation of the amplitude of the separation and reattachment point motions and thus for the low frequency breathing of the separation bubble. These results tend to suggest that the SWBLI unsteadiness is related to this low frequency dynamics of the recirculation bubble; the oscillations of the reflected shocks foot being in phase with the motion of the separation point
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Iampietro, David. "Contribution à la simulation d'écoulements diphasiques compressibles à faible vitesse en présence de sauts de pression par approches homogène et bi-fluide". Thesis, Aix-Marseille, 2018. http://www.theses.fr/2018AIXM0535/document.
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Les travaux de thèse sont axés sur les méthodes numériques pour les écoulements diphasiques, compressibles, à faible vitesse, avec apparition soudaine de forts gradients de pression. La vitesse matérielle de chacune des phases étant très petite devant la célérité des ondes acoustiques, le régime d'écoulement est dit à faible nombre de Mach. Dans ce travail, la loi d'état de la phase considérée contient toujours une information mesurant sa plus ou moins grande compressibilité. Ainsi, la faible compressibilité de l'eau peut produire un régime d'écoulement où des sauts de pression importants apparaissent même si le nombre de Mach est très faible. La première partie de la thèse s'est focalisée sur un modèle diphasique dit homogène-équilibré. Les deux phases de l'écoulement ont alors la même vitesse, pression, température et même potentiel chimique. Un premier travail a été la construction de solveurs de Riemann approchés dits tout-nombre-de-Mach. En l'absence de transitoire rapide, ces solveurs basent leur contrainte de pas de temps sur la vitesse des ondes matérielles lentes et sont donc précis pour suivre ces dernières. En revanche, lorsqu'une onde de choc rapide traverse l'écoulement, ces solveurs s'adaptent automatiquement afin de la capturer. La seconde partie de la thèse s'est focalisée sur la prise en compte du couplage convection-source dans le cadre des modèles en approche bi-fluides avec effets de relaxation pression-vitesse. Dans ces modèles, les deux phases de l'écoulement possèdent leur propre jeu de variables. Dans ce travail, un schéma implicite à mailles décalées, basé sur l'influence des termes sources dans des problèmes de Riemann linéaires, a été proposéThe present work focuses on numerical methods for low-material velocity compressible two-phase flows with high pressure jumps. In this context, the material velocity of both phases is small compared with the celerity of the acoustic waves. The flow is said to be a low-Mach number flow. In this work, the equation of state of the considered phase always contains information relative to its compressibility. For example, the low-compressibility of liquid water may lead to fast transients in which high pressure jumps are produced even if the flow Mach number is low. The first part of this work has leaned on two-phase homogeneous-equilibrium models. Thus, both phases have the same velocity, pressure, temperature and the same chemical potential. The construction of what is called an all-Mach-number approximate Riemann solver has been conducted. When no fast transients come through the flow, the above solvers enable computations with CFL conditions based on low-material velocities. As a result, they remain accurate to follow slow material interfaces, or subsonic contact discontinuities. However, when fast shock waves propagate, these solvers automatically adapt in order to capture them. The second part of the thesis has been dedicated to the design of numerical methods enhancing the coupling between convection and relaxation for two-fluid models containing pressure-velocity relaxation effects. In such models, both phases have their own set of variables. A time-implicit staggered scheme, based on the influence of relaxation source terms on linear Riemann problems has been proposed
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Sun, Hua. "Modélisation et simulation numérique de la convection naturelle dans des mélanges binaires de gaz parfaits contenus dans des cavités : application à la condensation ou à lévaporation surfaciques". Phd thesis, Université Paris-Est, 2010. http://tel.archives-ouvertes.fr/tel-00598321.
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L'objectif de c e mémoire est d'apporter une contribution à la modélisation et la simulation numérique de la convection thermosolutale de mélanges binaires de gaz parfaits contenus dans des cavités. Un modèle a été élaboré en se basant sur l'approximation de faible compressibilité. Le premier chapitre précise la démarche suivie dans la modélisation et une formulation originale en est déduite afin de traiter les différents types de conditions aux limites et de conditions de références hydrostatiques analysés dans le mémoire. Les variations de masse volumique sont déduites de la loi des gaz parfaits et la pression thermodynamique est calculée à partir de la conservation de la masse totale. La méthode numérique repose sur la méthode des volumes finis mise en uvre sur des maillages décalés. Le couplage vitesse-pression est traité par un nouvel algorithme dont l'efficacité est discutée en détail. La démarche numérique est validée via des comparaisons avec des solutions de références, en régime stationnaire comme en régime transitoire pour des écoulements transitionnels. Dans la seconde partie du mémoire, on considère d'abord la convection thermosolutale dans une cavité rectangulaire verticale dans le cas où les écoulements sont induits par des gradients horizontaux de température et de concentration. On discute en particulier les limites de l'approximation d'extrême dilution. La condensation de vapeur d'eau et l'évaporation d'un film d'eau liquide sur les parois d'une cavité sont ensuite étudiées en régime transitoire. Ces changements de phase surfaciques sont associés à la convection naturelle dans une cavité dont les températures des quatre parois varient au cours du temps
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Tang, Kunkun. "Combining Discrete Equations Method and Upwind Downwind-Controlled Splitting for Non-Reacting and Reacting Two-Fluid Computations". Phd thesis, Université de Grenoble, 2012. http://tel.archives-ouvertes.fr/tel-00819824.
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Lors que nous examinons numériquement des phénomènes multiphasiques suite à un accidentgrave dans le réacteur nucléaire, la dimension caractéristique des zones multi-fluides(non-réactifs et réactifs) s'avère beaucoup plus petite que celle du bâtiment réacteur, cequi fait la Simulation Numérique Directe de la configuration à peine réalisable. Autrement,nous proposons de considérer la zone de mélange multiphasique comme une interface infinimentfine. Puis, le solveur de Riemann réactif est inséré dans la Méthode des ÉquationsDiscrètes Réactives (RDEM) pour calculer le front de combustion à grande vitesse représentépar une interface discontinue. Une approche anti-diffusive est ensuite couplée avec laRDEM afin de précisément simuler des interfaces réactives. La robustesse et l'efficacité decette approche en calculant tant des interfaces multiphasiques que des écoulements réactifssont à la fois améliorées grâce à la méthode ici proposée : upwind downwind-controlled splitting(UDCS). UDCS est capable de résoudre précisément des interfaces avec les maillagesnon-structurés multidimensionnels, y compris des fronts réactifs de détonation et de déflagration.
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Corot, Théo. "Simulation numérique d'ondes de choc dans un milieu bifluide : application à l'explosion vapeur". Thesis, Paris, CNAM, 2017. http://www.theses.fr/2017CNAM1125/document.
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Cette thèse s'intéresse à la simulation numérique de l'explosion vapeur. Ce phénomène correspond à une vaporisation instantanée d'un volume d'eau liquide entraînant un choc de pression. Nous nous y intéressons dans le cadre de la sûreté nucléaire. En effet, lors d'un accident entraînant la fusion du cœur du réacteur, du métal fondu pourrait interagir avec de l'eau liquide et entraîner un tel choc. On voudrait alors connaître l'ampleur de ce phénomène et les risques d'endommagements de la centrale qu'il implique. Pour y parvenir, nous utilisons pour modèle les équations d'Euler dans un cadre Lagrangien. Cette description a l'avantage de suivre les fluides au cours du temps et donc de parfaitement conserver les interfaces entre l'eau liquide et sa vapeur. Pour résoudre numériquement les équations obtenues, nous développons un nouveau schéma de type Godunov utilisant des flux nodaux. Le solveur nodal développé durant cette thèse ne dépend que de la répartition angulaire des variables physiques autour du nœud. De plus, nous nous intéressons aux changements de phase liquide-vapeur. Nous proposons une méthode pour les prendre en compte et mettons en avant les avantages qu'il y a à l'implémentation de ce phénomène dans un algorithme LagrangienThis thesis studies numerical simulation of steam explosion. This phenomenon correspond to a fast vaporization of a liquid leading to a pressure shock. It is of interest in the nuclear safety field. During a core-meltdown crisis, molten fuel rods interacting with water could lead to steam explosion. Consequently we want to evaluate the risks created by this phenomenon.In order to do it, we use Euler equations written in a Lagrangian form. This description has the advantage of following the fluid motion and consequently preserves interfaces between the liquid and its vapor. To solve these equations, we develop a new Godunov type scheme using nodal fluxes. The nodal solver developed here only depends on the angular repartition of the physical variables around the node.Moreover, we study liquid-vapor phase changes. We describe a method to take it into account and highlight the advantages of using this method into a Lagrangian framework
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Raghavendra, Nandagiri Venkata. "Discrete Velocity Boltzmann Schemes for Inviscid Compressible Flows". Thesis, 2017. http://etd.iisc.ac.in/handle/2005/4314.
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It is known that high-speed flows are compressible. In large parts of the flow domains, the inviscid approximation is valid and this leads to Euler equations of gas dynamics. These inviscid compressible flows are modelled by coupled nonlinear hyperbolic systems of partial differential equations and generally require numerical solution techniques, as analytical solutions are usually not available.
Out of all the numerical methods developed over the past five decades to solve the Euler equations, the schemes based on kinetic theory of gases are elegant ones with distinct advantages of simplicity and robustness. However, many kinetic or Boltzmann schemes suffer from high dose of numerical diffusion and these methods are known to be less accurate. The exact shock capturing of steady grid-aligned discontinuities, achieved at the macroscopic level, is yet to be claimed by this class of methods. A closely related class of discrete velocity Boltzmann
schemes proved to be advantageous in this regard, with the first discrete kinetic scheme with exact shock capturing being introduced by Raghurama Rao and Balakrishna[51], by enforcing the Rankine-Hugoniot jump condition at the discrete level. In the first part of this thesis, this accurate shock capturing algorithm with a relaxation system is further improved by various techniques, such as including a diagonal matrix of coefficient of numerical diffusion for vector cases, introducing a wave speed correction mechanism for obtaining physically realistic solutions, introducing a limiter based variant to avoid the use of an entropy _x and finally modifying the numerical diffusion based on the entropy conservation equation to obtain a simple entropy stable and yet accurate discrete velocity Boltzmann scheme. The features of all the new variants are demonstrated by application to several bench-mark test problems.
In the second part of the thesis, a discrete velocity Boltzmann scheme which can capture steady contact discontinuities exactly is developed by using the generalized Riemann invariants together with the jump conditions. This scheme is accurate and widely applicable, without the need for any entropy correction, the relevant features being demonstrated by application to several benchmark test problems.
In the third part of this thesis, a discrete velocity Boltzmann scheme is developed by using physically relevant discrete velocities. A derivation introduced by Sanders and Prendergast [58] is modified to introduce the velocities, of the Dirac delta functions which replace the Maxwellian, matching the eigenvalues at the macroscopic level. This strategy is further coupled with the framework of a discrete velocity Boltzmann system to develop an efficient relaxation scheme for solving the Euler equations. This new algorithm is found to be low in numerical diffusion and also successful in handling various challenging test problems.
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Ghosh, Ashis Kumar. "Robust Least Squares Kinetic Upwind Method For Inviscid Compressible Flows". Thesis, 1996. https://etd.iisc.ac.in/handle/2005/1570.
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Ghosh, Ashis Kumar. "Robust Least Squares Kinetic Upwind Method For Inviscid Compressible Flows". Thesis, 1996. http://etd.iisc.ernet.in/handle/2005/1570.
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43
Felthum, Luke T. "Finite element analysis of compressible flows". Thesis, 1995. https://hdl.handle.net/10539/24374.
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A dissertation submitted to the Faculty of Engineering, University of the Witwatersrand,
Johannesburg, in fulfilment of the requirements for the degree of Master of Science in
Engineering.In this research a finite element analysis program was developed for the modelling of general compressible Euler flows. An explicit Taylor-Galerkin algorithm was used as the flow solver and was used in conjunction with a flux-corrected transport algorithm in order to obtain high shock resolution without numerical oscillations and overshoots. The solver was applied to two and three dimensional geometries. An axisymmetric extension of the Taylor Galerkin algorithm was also developed. For the two dimensional code, a fully automatic mesh generator was implemented which was able to generate meshes for completely arbitrary geometries, as well as an adaptive refinement algorithm which performs an error analysis on the solution and refines and coarsens the mesh appropriately in order to maintain an optimal mesh resolution. The automatic mesh generator dramatically reduced problem setup time and the adaptive refinement algorithm reduced compllter time by up to 90%" A number of test cases were performed covering a wide range of compressible flows including steady and unsteady flows in air, using the ideal gas model, and shocks in liquids, using the Tait model. Within the limitations of the inviscid and real gas assumptions made, accurate results were obtained,
AC 2018
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Thoren, Elizabeth Erin. "Linear instability for incompressible inviscid fluid flows : two classes of perturbations". 2009. http://hdl.handle.net/2152/6571.
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One approach to examining the stability of a fluid flow is to linearize the
evolution equation at an equilibrium and determine (if possible) the stability
of the resulting linear evolution equation. In this dissertation, the space of
perturbations of the equilibrium flow is split into two classes and growth of
the linear evolution operator on each class is analyzed. Our classification of
perturbations is most naturally described in V.I. Arnold’s geometric view of
fluid dynamics. The first class of perturbations we examine are those that
preserve the topology of vortex lines and the second class is the factor space
corresponding to the first class. In this dissertation we establish lower bounds
for the essential spectral radius of the linear evolution operator restricted to
each class of perturbations.text
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"Some topics on compressible flows in nozzles". Thesis, 2007. http://library.cuhk.edu.hk/record=b6074443.
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Finally, we discuss some open problems closely related to the results obtained in this thesis and give some perspectives.First, we study global subsonic and subsonic-sonic potential flows through a general infinitely long two dimensional or three dimensional axially symmetric nozzle. It is proved that there exists a critical value for the incoming mass flux so that a global uniformly subsonic flow exists in the nozzle as long as the incoming mass flux is less than the critical value. Furthermore, we establish some uniform estimates for the deflection angles and the minimum speed of the subsonic flows by combining the hodograph transformation and the comparison principle for elliptic equations. With the help of these properties and a compensated compactness framework, we prove the existence of a global subsonic-sonic flow solution in the case of the critical incoming mass flux.
Second, global existence of steady subsonic Euler flows through infinitely long nozzles is established when the variation of Bernoulli's constant in the upstream is sufficiently small and mass flux is in a suitable regime with an upper critical value. One of the main difficulties lies in that the full steady Euler system is a hyperbolic-elliptic coupled system in a subsonic region. A key point is to use stream function formulation for compressible Euler equations. By this formulation, Euler equations are equivalent to a quasilinear second order equation for stream function. We obtain existence of solution to the boundary value problem for stream function with the help of estimate for elliptic equation of two variables. Asymptotic behavior for the stream function is obtained via a blow up argument and energy estimate. This asymptotic behavior, together with some refined estimates on the stream function, yields the consistency of the stream function formulation and the original Euler equations.
Xie, Chunjing.
"August 2007."
Adviser: Zhouping Xin.
Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1075.
Thesis (Ph.D.)--Chinese University of Hong Kong, 2007.
Includes bibliographical references (p. 139-140).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstract in English and Chinese.
School code: 1307.
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Kotnala, Sourabh. "Lattice Boltzmann Relaxation Scheme for Compressible Flows". Thesis, 2012. http://etd.iisc.ac.in/handle/2005/3257.
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Lattice Boltzmann Method has been quite successful for incompressible
flows. Its extension for compressible (especially supersonic and hypersonic)
flows has attracted lot of attention in recent time. There have been some
successful attempts but nearly all of them have either resulted in complex
or expensive equilibrium function distributions or in extra energy levels.
Thus, an efficient Lattice Boltzmann Method for compressible fluid flows
is still a research idea worth pursuing for. In this thesis, a new Lattice
Boltzmann Method has been developed for compressible flows, by using the concept of a relaxation system, which is traditionally used as semilinear alternative for non-linear hypebolic systems in CFD. In the relaxation
system originally introduced by Jin and Xin (1995), the non-linear flux in a hyperbolic conservation law is replaced by a new variable, together with a relaxation equation for this new variable augmented by a
relaxation term in which it relaxes to the original nonlinear flux, in the limit of a vanishing relaxation parameter. The advantage is that instead of one non-linear hyperbolic equation, two linear hyperbolic equations need to be solved, together with a non-linear relaxation term. Based on the interpretation
of Natalini (1998) of a relaxation system as a discrete velocity Boltzmann equation, with a new isotropic relaxation system as the basic building block, a Lattice Boltzmann Method is introduced for solving the
equations of inviscid compressible flows. Since the associated equilibrium
distribution functions of the relaxation system are not based on a low Mach
number expansion, this method is not restricted to the incompressible limit.
Free slip boundary condition is introduced with this new relaxation system
based Lattice Boltzmann method framework. The same scheme is then extended
for curved boundaries using the ghost cell method. This new Lattice Boltzmann Relaxation Scheme is successfully tested on various bench-mark test cases for solving the equations of compressible flows such as shock tube problem in 1-D and in 2-D the test cases involving supersonic flow over a forward-facing step, supersonic oblique shock reflection from a flat plate, supersonic and hypersonic flows past half-cylinder.
47
Kotnala, Sourabh. "Lattice Boltzmann Relaxation Scheme for Compressible Flows". Thesis, 2012. http://hdl.handle.net/2005/3257.
Pełny tekst źródłaStreszczenie:
Lattice Boltzmann Method has been quite successful for incompressible
flows. Its extension for compressible (especially supersonic and hypersonic)
flows has attracted lot of attention in recent time. There have been some
successful attempts but nearly all of them have either resulted in complex
or expensive equilibrium function distributions or in extra energy levels.
Thus, an efficient Lattice Boltzmann Method for compressible fluid flows
is still a research idea worth pursuing for. In this thesis, a new Lattice
Boltzmann Method has been developed for compressible flows, by using the concept of a relaxation system, which is traditionally used as semilinear alternative for non-linear hypebolic systems in CFD. In the relaxation
system originally introduced by Jin and Xin (1995), the non-linear flux in a hyperbolic conservation law is replaced by a new variable, together with a relaxation equation for this new variable augmented by a
relaxation term in which it relaxes to the original nonlinear flux, in the limit of a vanishing relaxation parameter. The advantage is that instead of one non-linear hyperbolic equation, two linear hyperbolic equations need to be solved, together with a non-linear relaxation term. Based on the interpretation
of Natalini (1998) of a relaxation system as a discrete velocity Boltzmann equation, with a new isotropic relaxation system as the basic building block, a Lattice Boltzmann Method is introduced for solving the
equations of inviscid compressible flows. Since the associated equilibrium
distribution functions of the relaxation system are not based on a low Mach
number expansion, this method is not restricted to the incompressible limit.
Free slip boundary condition is introduced with this new relaxation system
based Lattice Boltzmann method framework. The same scheme is then extended
for curved boundaries using the ghost cell method. This new Lattice Boltzmann Relaxation Scheme is successfully tested on various bench-mark test cases for solving the equations of compressible flows such as shock tube problem in 1-D and in 2-D the test cases involving supersonic flow over a forward-facing step, supersonic oblique shock reflection from a flat plate, supersonic and hypersonic flows past half-cylinder.
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Welter, Roland Kuha. "Asymptotic approximation of fluid flows from the compressible Navier-Stokes equations". Thesis, 2021. https://hdl.handle.net/2144/42958.
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In this thesis a method for studying the asymptotic behavior of solutions to dissipative partial differential equations is developed, motivated by the study of the compressible Navier-Stokes equations in the past works of Hoff and Zumbrun,1995, Hoff and Zumbrun, 1997. In its most basic form, this method allows one to compute n^th order approximations in terms of Hermite functions of solutions of the heat equation having n^th order moments. The main advantage is that these approximations can be efficiently computed, and are often given explicitly in terms of elementary functions. It is shown how this method can be extended to increasingly complicated systems, leading the way toward the asymptotic analysis of the compressible Navier-Stokes equations.
A number of challenges must be overcome to apply this method to the compressible Navier-Stokes system. For technical reasons, the analysis is carried out on the divergence and curl of the velocity field, and hence a means of recovering the velocity field from these quantities is established first. The linear part of the evolution is then studied, and an extended version of the artificial viscosity decomposition previously developed (Kawashima, Hoff and Zumbrun1995) is introduced. This decomposition is in terms of the heat and combined heat-wave operators, and hence general estimates on their evolution in weighted L^p spaces are obtained.
A modified compressible Navier-Stokes system is then introduced which captures the dominant behavior of the linear evolution and possesses similar nonlinear terms. Solutions to this modified system are proven to exist in weighted spaces, showing that solutions initially having a certain number of moments possess this same number of moments for all time. An analysis of the asymptotic behavior of the modified compressible Navier-Stokes system is then carried out, and it is shown that the method developed herein extends and unifies the approach of Hoff and Zumbrun with that of Gallay and Wayne, 2002a, Gallay and Wayne, 2002b, where it was originally developed to study the behavior of the incompressible Navier-Stokes equations. The thesis is concluded with a discussion of how the results obtained for the modified compressible Navier-Stokes system pave the way for an analysis of the true compressible Navier-Stokes system, the generalization of this asymptotic analysis to arbitrary order, and with a comparison of this asymptotic analysis to that found in the recent work of Kagei and Okita, 2017.
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Deka, Mandeep. "Stability of wall-bounded compressible shear flows". Thesis, 2023. https://etd.iisc.ac.in/handle/2005/6163.
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In this work, the linear stability of compressible shear flows in channels and pipes are studied. A steady fully-developed laminar flow of an ideal gas, driven in a channel and a pipe by a constant body acceleration, is considered as the base state. The base flow profiles, being functions of Mach number, are obtained through numerical solution of the Navier-Stokes equations under steady parallel-flow conditions. Small amplitude normal mode perturbations are added to this flow and temporally growing solutions are studied. The evolution equations for the normal modes, that form a linear eigenvalue problem, are solved numerically by Chebyshev-Pseudospectral method.
For both channel and pipe flows, the eigenspectra show presence of compressible higher modes that do not have a counterpart in the incompressible limit. These modes are categorised into two distinct families based on the variation of the real part of their wave-speed with stream-wise wave-number. Numerical studies show the dominant instability at finite Mach numbers to be due to the modes that show a monotonic increase in the real part of the wave-speed with wave-number. These modes become unstable at finite wave-numbers at Mach numbers above a critical value. We have extended the classical stability theorems to compressible flows in bounded domains. A new criteria for the existence of neutral modes is derived which is used to obtain the values of the critical Mach numbers for the stability of the higher compressible modes.
In the incompressible limit, a pipe flow is stable to all modal perturbations, but the channel flow is unstable to the Tollmien-Schlichting (T-S) mode. Numerical studies at finite Mach numbers show compressibility to have a stabilising effect on the T-S mode. The critical Reynolds numbers as a function of Mach number are obtained for the all the unstable modes in both channel and pipe flows. A universal scaling of the critical values is shown at high Mach numbers. The critical Reynolds numbers for three-dimensional disturbances are also calculated for a compressible channel flow. It is shown that oblique waves are more unstable than two-dimensional waves with the minimum critical Reynolds number appearing at a specific wave-angle corresponding to a particular Mach number.
Numerical calculations of the stability equations are also performed in the inviscid limit where the numerical contour of integration is suitably chosen to avoid the branch point singularity at the critical point. The inviscid limit of the dominant compressible modes in channel and pipe flows compared against the high Reynolds number viscous calculations reveal the instabilities to be viscous in nature. The instability in channel and pipe flow appear due to a change in the viscous wall layer due to the emergence of a critical point very close to the wall.
The unstable modes in channel and pipe flows are studied at high Reynolds numbers through an asymptotic analysis. The instabilities in compressible channel flow are categorised into a small wave-number mode, which is the finite Mach number extension of the T-S mode, and finite wave-number modes, which are the dominant compressible higher modes. The asymptotic analysis for the lower and upper branches of the stability curve are performed to obtain the scalings for the wave-number, wave-speed, as well as the wall layer scalings for viscous regularization. An adjoint-based procedure imposing the solvability condition on the first and second correction to the stability equations, is devised to obtain the leading order eigenvalues for the lower and upper branches at high Reynolds numbers. The same asymptotic analysis is performed for the finite wave-number modes of the compressible pipe flow as well.
We also study the stability of a compressible flow in a channel with compliant walls. The compliant walls are modelled as spring-backed plates that move in the direction normal to the flow due to the fluid stresses acting at the walls. Wall compliance introduces additional instabilities, referred to as FSI modes, in addition to the Tollmien-Schlichting and compressible higher modes. The numerical studies indicate flow compressibility to have a stabilising effect on the FSI modes, and wall compliance to have a stabilising role on the compressible higher modes. Both flow compressibility and wall compliance are observed to have a stabilising effect on the Tollmien-Schlichting mode. We also calculate the perturbation energy budgets for the different instabilities which allow us to differentiate the different mechanisms of destabilisation of these modes.
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"A novel macro particle method for compressible flows: graphics and fluid dynamics applications". 2003. http://library.cuhk.edu.hk/record=b6073620.
Pełny tekst źródłaStreszczenie:
Kar Ki Chan."November 2003."
Thesis (Ph.D.)--Chinese University of Hong Kong, 2003.
Includes bibliographical references (p. 104-113).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Mode of access: World Wide Web.
Abstracts in English and Chinese.