Relevant bibliographies by topics / 2D Compressible Euler

Academic literature on the topic '2D Compressible Euler'

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Published: 11 March 2023

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Journal articles on the topic "2D Compressible Euler"

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Buckmaster, Tristan, and Sameer Iyer. "Formation of Unstable Shocks for 2D Isentropic Compressible Euler." Communications in Mathematical Physics 389, no. 1 (November 30, 2021): 197–271. http://dx.doi.org/10.1007/s00220-021-04271-z.

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Yuen, Manwai. "Vortical and self-similar flows of 2D compressible Euler equations." Communications in Nonlinear Science and Numerical Simulation 19, no. 7 (July 2014): 2172–80. http://dx.doi.org/10.1016/j.cnsns.2013.11.008.

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Zhang, Huali. "Local existence with low regularity for the 2D compressible Euler equations." Journal of Hyperbolic Differential Equations 18, no. 03 (September 2021): 701–28. http://dx.doi.org/10.1142/s0219891621500211.

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We prove the local existence, uniqueness and stability of local solutions for the Cauchy problem of two-dimensional compressible Euler equations, where the initial data of velocity, density, specific vorticity [Formula: see text] and the spatial derivative of specific vorticity [Formula: see text].
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Bressan, Alberto, Yi Jiang, and Hailiang Liu. "Numerical study of non-uniqueness for 2D compressible isentropic Euler equations." Journal of Computational Physics 445 (November 2021): 110588. http://dx.doi.org/10.1016/j.jcp.2021.110588.

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Godin, Paul. "The 2D compressible Euler equations in bounded impermeable domains with corners." Memoirs of the American Mathematical Society 269, no. 1313 (January 2021): 0. http://dx.doi.org/10.1090/memo/1313.

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Sun, Meina, and Chun Shen. "On the Riemann problem for 2D compressible Euler equations in three pieces." Nonlinear Analysis: Theory, Methods & Applications 70, no. 11 (June 2009): 3773–80. http://dx.doi.org/10.1016/j.na.2008.07.033.

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Baldauf, Michael. "Linear Stability Analysis of Runge–Kutta-Based Partial Time-Splitting Schemes for the Euler Equations." Monthly Weather Review 138, no. 12 (December 1, 2010): 4475–96. http://dx.doi.org/10.1175/2010mwr3355.1.

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Abstract For atmospheric simulation models with resolutions from about 10 km to the subkilometer cloud-resolving scale, the complete nonhydrostatic compressible Euler equations are often used. An important integration technique for them is the time-splitting (or split explicit) method. This article presents a comprehensive numerical stability analysis of Runge–Kutta (RK)-based partial time-splitting schemes. To this purpose a linearized two-dimensional (2D) compressible Euler system containing advection (as the slow process), sound, and gravity wave terms (as fast processes) is considered. These processes are the most important ones in limiting stability. First, the detailed stability properties are discussed with regard to several off-centering weights for each fast process described by horizontally explicit, vertically implicit schemes. Then the stability properties of the temporally and spatially discretized three-stage RK scheme for the complete 2D Euler equations and their stabilization (e.g., by divergence damping) are discussed. The main goal is to find optimal values for all of the occurring numerical parameters to guarantee stability in operational model applications. Furthermore, formal orders of temporal truncation errors for the time-splitting schemes are calculated. With the same methodology, two alternatives to the three-stage RK method, a so-called RK3-TVD method, and a new four-stage, second-order RK method are inspected.
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Arnold, Anton, and Ulrich Giering. "An Analysis of the Marshak Conditions for Matching Boltzmann and Euler Equations." Mathematical Models and Methods in Applied Sciences 07, no. 04 (June 1997): 557–77. http://dx.doi.org/10.1142/s0218202597000293.

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Domain decomposition methods based on matching the Boltzmann and Euler equations without overlapping are an important simulation technique in rarefied gas dynamics and semiconductor device modeling. Many existing codes use the Marshak boundary conditions (i.e. imposing continuity of the fluxes) at the interface between the two modeling regimes to implicitly determine the boundary data for the compressible Euler equations. In this paper we investigate the solvability of the Marshak conditions in the four different flow situations sub-/supersonic in-/outflow in one spacial dimension and for selected cases in 2D and 3D.
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Liu, Tiegang, A. W. Chowdhury, and Boo Cheong Khoo. "The Modified Ghost Fluid Method Applied to Fluid-Elastic Structure Interaction." Advances in Applied Mathematics and Mechanics 3, no. 5 (October 2011): 611–32. http://dx.doi.org/10.4208/aamm.10-m1054.

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AbstractIn this work, the modified ghost fluid method is developed to deal with 2D compressible fluid interacting with elastic solid in an Euler-Lagrange coupled system. In applying the modified Ghost Fluid Method to treat the fluid-elastic solid coupling, the Navier equations for elastic solid are cast into a system similar to the Euler equations but in Lagrangian coordinates. Furthermore, to take into account the influence of material deformation and nonlinear wave interaction at the interface, an Euler-Lagrange Riemann problem is constructed and solved approximately along the normal direction of the interface to predict the interfacial status and then define the ghost fluid and ghost solid states. Numerical tests are presented to verify the resultant method.
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Hou, Fei, and Huicheng Yin. "On global axisymmetric solutions to 2D compressible full Euler equations of Chaplygin gases." Discrete & Continuous Dynamical Systems - A 40, no. 3 (2020): 1435–92. http://dx.doi.org/10.3934/dcds.2020083.

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Dissertations / Theses on the topic "2D Compressible Euler"

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DOLCE, MICHELE. "Linear stability analysis of stationary Euler flows for passive scalars and inhomogeneous fluids." Doctoral thesis, Gran Sasso Science Institute, 2020. http://hdl.handle.net/20.500.12571/15111.

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This thesis is concerned with the study of linear stability properties of some particular fluid flows, within the framework of quantitative hydrodynamic stability. In the last decade, the problem has received a lot of attention thanks to the introduction of new analytical techniques particularly useful to tackle classical problems that date back to the end of the nineteen century. The purpose of this thesis is threefold. We first investigate the asymptotic decay properties of a passive scalar driven by a vortex with a power-law velocity field in the whole plane. In particular, we quantify the enhanced dissipation mechanism caused by fluid mixing, namely, the transfer of energy from large to small scales due to transport. We provide sharp (up to a logarithmic correction) bounds on the dissipation time-scales, which are faster than the standard diffusive one. The rest of the thesis is dedicated to the study of the stability of parallel flows in 2D inhomogeneous fluids. The second problem we deal with concerns a linear stability analysis for the Couette flow with constant density in an isentropic compressible fluid. We consider both the inviscid and the viscous case. In the inviscid case, we give the first rigorous mathematical justification to a Lyapunov instability mechanism previously addressed in the physics literature. More precisely, we show that the L^2 norms of the density and the irrotational component of the velocity field grow as t^(1/2) Instead, the solenoidal component of the velocity strongly converges to zero in L^2, a mechanism known as inviscid damping. In the viscous case, we present the first enhanced dissipation result for an inhomogeneous fluid. The exponential decay become effective on a time-scale O( u^(-1/3)), with u being proportional to the inverse of the Reynolds number, and there is a large transient growth of order O( u^(-1/6)) caused by the inviscid instability. The estimates are valid also in a large Mach number regime. We finally study the stability of a particular class of stratified shear flows. We consider an inhomogeneous, inviscid and incompressible fluid under the action of gravity, near shear flows close to Couette with an exponentially stratified density profile. Under the Miles-Howard criterion, we prove the inviscid damping for the velocity field and the (scaled) density. The decay rates are slower with respect to the classical homogeneous case without gravity. This is due to a Lyapunov instability mechanism for the vorticity that we characterize in the Couette case.
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Zingan, Valentin Nikolaevich. "Discontinuous Galerkin Finite Element Method for the Nonlinear Hyperbolic Problems with Entropy-Based Artificial Viscosity Stabilization." Thesis, 2012. http://hdl.handle.net/1969.1/ETD-TAMU-2012-05-10845.

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This work develops a discontinuous Galerkin finite element discretization of non- linear hyperbolic conservation equations with efficient and robust high order stabilization built on an entropy-based artificial viscosity approximation. The solutions of equations are represented by elementwise polynomials of an arbitrary degree p > 0 which are continuous within each element but discontinuous on the boundaries. The discretization of equations in time is done by means of high order explicit Runge-Kutta methods identified with respective Butcher tableaux. To stabilize a numerical solution in the vicinity of shock waves and simultaneously preserve the smooth parts from smearing, we add some reasonable amount of artificial viscosity in accordance with the physical principle of entropy production in the interior of shock waves. The viscosity coefficient is proportional to the local size of the residual of an entropy equation and is bounded from above by the first-order artificial viscosity defined by a local wave speed. Since the residual of an entropy equation is supposed to be vanishingly small in smooth regions (of the order of the Local Truncation Error) and arbitrarily large in shocks, the entropy viscosity is almost zero everywhere except the shocks, where it reaches the first-order upper bound. One- and two-dimensional benchmark test cases are presented for nonlinear hyperbolic scalar conservation laws and the system of compressible Euler equations. These tests demonstrate the satisfactory stability properties of the method and optimal convergence rates as well. All numerical solutions to the test problems agree well with the reference solutions found in the literature. We conclude that the new method developed in the present work is a valuable alternative to currently existing techniques of viscous stabilization.
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Books on the topic "2D Compressible Euler"

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Godin, Paul. 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners. American Mathematical Society, 2021.

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Conference papers on the topic "2D Compressible Euler"

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Verhoff, A. "Analytical Euler Solution for 2D Compressible Airfoil Flow." In 41st Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2003. http://dx.doi.org/10.2514/6.2003-427.

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WANG, LIXIA, and DAVID CAUGHEY. "A multiblock/multigrid Euler method to simulate 2D and 3D compressible flow." In 31st Aerospace Sciences Meeting. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1993. http://dx.doi.org/10.2514/6.1993-332.

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Verhoff, A. "Analytical Euler solution for 2D compressible ramp flow with experimental data comparison." In Fluids 2000 Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2000. http://dx.doi.org/10.2514/6.2000-2230.

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Camp, Joshua L., and Andrew Duggleby. "Compressible Euler Extension of a Massively-Parallel Spectral Element Solver." In ASME 2012 Fluids Engineering Division Summer Meeting collocated with the ASME 2012 Heat Transfer Summer Conference and the ASME 2012 10th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/fedsm2012-72308.

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Current supercomputing systems have tens or hundreds of thousands of cores and are trending to GPU and co-compute platforms that deliver thousands of cores per node. Modern computational fluid dynamics codes must be designed to take advantage of these developments in order to further their use in the design cycle. Furthermore, these codes must be highly accurate, stable, and geometrically flexible. NEK5000 is a massively-parallel spectral element code that exhibits these characteristics but currently only for incompressible and low-Mach flows. Adding capabilities for NEK5000 to solve the fully compressible Navier-Stokes equations will extend its usefulness to aerospace applications. As a first step the following work extends NEK5000’s capabilities to solve the 2D compressible Euler equations. Using the conservative formulation, the equations are discretized using a non-staggered spectral element mesh, and the state variables are advanced using 1st order explicit Euler time stepping. A channel with a 10% bump is used as a test case for the modification. The modified NEK5000 code performs very well despite not being optimized for use in hyperbolic equations.
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Caggio, M., B. Ducomet, Š. Nečasová, and T. Tang. "On the Problem of Singular Limit." In Topical Problems of Fluid Mechanics 2023. Institute of Thermomechanics of the Czech Academy of Sciences; CTU in Prague Faculty of Mech. Engineering Dept. Tech. Mathematics, 2023. http://dx.doi.org/10.14311/tpfm.2023.002.

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We consider the problem of singular limit of the compressible Euler system confined to a straight layer Ωδ = (0, δ)×R², δ > 0. In the regime of low Mach number limit and reduction of dimension the convergence to the strong solution of the 2D incompressible Euler system is shown.
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Marques, Nelson P. C., and José C. F. Pereira. "Compressible Fluid Flow and Heat Transfer Navier-Stokes Predictions on Unstructured Grids." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-0861.

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Abstract A second-order accurate finite volume method for solving compressible 2D flows on hybrid structured-unstructured grids is presented. Separate reconstruction and evolution steps are taken to discretize the convective terms. For the reconstruction step, a data-dependent Least-Squares procedure is used, while for the evolution step two recent flux functions are included: the HLLC approximate Riemann solver and the AUSM+ flux vector splitting. Steady-state solutions are obtained with an implicit backward Euler scheme. The assembled system is solved by iterative means (BiCGSTAB, GMRES) with ILU pre-conditioning. Two internal, steady, 2D flow test cases are presented to validate the code: a supersonic 10° ramp inside a channel and a laminar flow through a double-throated nozzle. The code proved accurate with the use of both flux functions when comparing the computed results with both an analytical (ramp) and a reference solution (nozzle). The GMRES solver generally required less CPU time until convergence for the inviscid test-case while the BiCGSTAB solver got the edge for the viscous calculations.
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Karbalaei, Alireza, and Kazem Hejranfar. "A Central Difference Finite Volume Lattice Boltzmann Method for Simulation of 2D Inviscid Compressible Flows on Triangular Meshes." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86302.

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In this work, a central difference finite volume lattice Boltzmann method (CDFV-LBM) is developed to compute 2D inviscid compressible flows on triangular meshes. The numerical solution procedure adopted here for solving the lattice Boltzmann equation is nearly the same as the procedure used by Jameson et al. for the solution of the Euler equations. The integral form of the lattice Boltzmann equation using the Gauss divergence theorem is applied on a triangular cell and the numerical fluxes on each edge of the cell are set to the average of their values at the two adjacent cells. Appropriate numerical dissipation terms are added to the discretized lattice Boltzmann equation to have a stable solution. The Boltzmann equation is discretized in time using the fourth-order Runge-Kutta scheme. The computations are performed for three problems, namely, the isentropic vortex and the supersonic flow around a NACA0012 airfoil and over a circular-arc bump. The effect of changing the grid resolution and the dissipation coefficients on the accuracy of the results is also studied. Results obtained by applying the CDFV-LBM are compared with the available numerical results which show good agreement.
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Chen, Weixiong, Yangang Wang, Hao Wang, Shuanghou Deng, and Haiqi Qin. "A Three-Dimensional Analytical Stability Model of Contra-Rotating Compressors Based on Partial Simplification of Euler Equation." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-76322.

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The present study developed a three-dimensional compressible analytical model for predicting the rotating stall boundary in turbomachinery. Based on the small perturbation theory and the inviscid Euler equation. Using the perturbation wave dispersion theory and boundary conditions, the problem of stall prediction in turbomachinery can be regarded as the solution of the matrix eigenvalue problem. To validate the feasibility and accuracy of the developed analytical model. After that, the NASA Rotor 67 and NASA Stage 35, which have been disclosed in detail, are selected to validate the 3D analytical model. Results has been successfully verified the accuracy of the developed prediction model. Meanwhile, the advantages of the 3D analytical model, which considers the radial mainstream velocity and disturbance velocity are also demonstrated in comparison with the 2D model developed by Ludwig et al. Finally, the three-dimensional analytical model is used to predict the stall boundary of a contra-rotating compressor test rig. Results show that the downstream rotor encounters rotating stall firstly, and the stall mass flow is about 5.871kg/ s. A good agreement has been also revealed from the unsteady numerical simulation and thus again evidence the ability of the developed three-dimensional analytical model in terms of accuracy and efficiency.
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Escobar, Sergio, Suryanarayana R. Pakalapati, Ismail Celik, Donald Ferguson, and Peter Strakey. "Numerical Investigation of Rotating Detonation Combustion in Annular Chambers." In ASME Turbo Expo 2013: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/gt2013-94918.

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This article presents two dimensional (2D) and three-dimensional (3D) computational analysis of rotating detonation combustion (RDC) in annular chambers using the commercial computational fluid dynamics (CFD) solver ANSYS-Fluent V13. The applicability of ANSYS-Fluent to predict the predominant phenomena taking place in the combustion chamber of a rotating detonation combustor is assessed. Simulations are performed for stoichiometric Hydrogen-Air combustion using two different chemical mechanisms. First, a widely used one-step reaction mechanism that uses mass fraction of the reactant as a progress variable, then a reduced chemical mechanism for H2-Air combustion including NOx chemistry was employed. Time dependent 2D and 3D simulations are carried out by solving Euler equations for compressible flows coupled with chemical reactions. Fluent user defined functions (UDF) were constructed and integrated into the commercial CFD solver in order to model the micro nozzle and slot injection system for fuel and oxidizer, respectively. Predicted pressure and temperature fields and detonation wave velocities are compared for the two reaction mechanisms. Curvature effects on the properties of transverse detonation waves are studied by comparing the 2D and 3D simulations. The effects of diffusion terms on RDC phenomena are assessed by solving full Navier-Stokes equations and comparing the results with those from Euler equations. Computational results are compared with experimentally measured pressure data obtained from the literature. Results show that the detonation wave velocity is over predicted in all the simulations. However, good agreement between computational and experimental data for the pressure field and transverse detonation wave structure proves adequate capabilities of ANSYS-Fluent to predict the main physical characteristics of RDC operation. Finally, various improvements for RDC modeling are postulated, particularly for better prediction of wave velocity.
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Laubscher, Ryno, Pieter Rousseau, and Chris Meyer. "Modeling of Inviscid Flow Shock Formation in a Wedge-Shaped Domain Using a Physics-Informed Neural Network-Based Partial Differential Equation Solver." In ASME Turbo Expo 2022: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/gt2022-81768.

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Abstract Physics-informed neural networks (PINN) can potentially be applied to develop computationally efficient surrogate models, perform anomaly detection, and develop time-series forecasting models. However, predicting small-scale features such as the exact location of shocks and the associated rapid changes in fluid properties across it, have proven to be challenging when using standard PINN architectures, due to spatial biasing during network training. This paper investigates the ability of PINNs to capture these features of an oblique shock by applying Fourier feature network architectures. Four PINN architectures are applied namely a standard PINN architecture with the direct and indirect implementation of the ideal gas equation of state, as well as the direct implementation combined with a standard and modified Fourier feature transformation function. The case study is 2D steady-state compressible Euler flow over a 15° wedge at a Mach number of 5. The PINN predictions are compared to results generated using proven numerical CFD techniques. The results show that the indirect implementation of the equation of state is unable to enforce the prescribed boundary conditions. The application of the Fourier feature up-sampling to the low-dimensional spatial coordinates improves the ability of the PINN model to capture the small-scale features, with the standard implementation performing better than the modified version.
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