Relevant bibliographies by topics / Divergence-free method

Academic literature on the topic 'Divergence-free method'

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Published: 2 September 2023

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Journal articles on the topic "Divergence-free method"

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Huerta, Antonio, Yolanda Vidal, and Pierre Villon. "Pseudo-divergence-free element free Galerkin method for incompressible fluid flow." Computer Methods in Applied Mechanics and Engineering 193, no. 12-14 (March 2004): 1119–36. http://dx.doi.org/10.1016/j.cma.2003.12.010.

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Klingenberg, Christian, Frank Pörner, and Yinhua Xia. "An Efficient Implementation of the Divergence Free Constraint in a Discontinuous Galerkin Method for Magnetohydrodynamics on Unstructured Meshes." Communications in Computational Physics 21, no. 2 (February 2017): 423–42. http://dx.doi.org/10.4208/cicp.180515.230616a.

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AbstractIn this paper we consider a discontinuous Galerkin discretization of the ideal magnetohydrodynamics (MHD) equations on unstructured meshes, and the divergence free constraint (∇·B=0) of its magnetic field B. We first present two approaches for maintaining the divergence free constraint, namely the approach of a locally divergence free projection inspired by locally divergence free elements [19], and another approach of the divergence cleaning technique given by Dedner et al. [15]. By combining these two approaches we obtain a efficient method at the almost same numerical cost. Finally, numerical experiments are performed to show the capacity and efficiency of the scheme.
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Avdeeva, E. N., and V. V. Lukin. "Divergence-free finite-difference method for 2D ideal MHD." Journal of Physics: Conference Series 1336 (November 2019): 012026. http://dx.doi.org/10.1088/1742-6596/1336/1/012026.

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Fu, Guosheng. "An Explicit Divergence-Free DG Method for Incompressible Magnetohydrodynamics." Journal of Scientific Computing 79, no. 3 (January 14, 2019): 1737–52. http://dx.doi.org/10.1007/s10915-019-00909-2.

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Fu, Guosheng. "An explicit divergence-free DG method for incompressible flow." Computer Methods in Applied Mechanics and Engineering 345 (March 2019): 502–17. http://dx.doi.org/10.1016/j.cma.2018.11.012.

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Li, Shengtai. "A fourth-order divergence-free method for MHD flows." Journal of Computational Physics 229, no. 20 (October 2010): 7893–910. http://dx.doi.org/10.1016/j.jcp.2010.06.044.

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Zhang, Man, and Xueshang Feng. "A Three-Order, Divergence-Free Scheme for the Simulation of Solar Wind." Universe 8, no. 7 (July 5, 2022): 371. http://dx.doi.org/10.3390/universe8070371.

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In this paper, we present a three-order, divergence-free finite volume scheme to simulate the steady state solar wind ambient. The divergence-free condition of the magnetic field is preserved by the constrained transport (CT) method. The CT method can keep the magnetic fields divergence free if the magnetic fields is divergence free initially. Thus, a least-squares reconstruction of magnetic field with the divergence free constraints is used to make the magnetic fields global solenoidality initially. High order spatial accuracy is obtained through a non-oscillatory hierarchical reconstruction, while a high order time discretization is achieved using a three-order Runge–Kutta scheme. This new model of three order in space and time is validated by numerical results for Carrington rotation 2207. The numerical results show its capability for producing stable reliable results for structured solar wind. The high-order, divergence-free properties of this method make it an ideal tool for the simulations of coronal mass ejection in future.
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Deng, Yongbo, and Jan G. Korvink. "Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2189 (May 2016): 20150835. http://dx.doi.org/10.1098/rspa.2015.0835.

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This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.
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Qin, Si-xue. "A divergence-free method to extract observables from correlation functions." Physics Letters B 742 (March 2015): 358–62. http://dx.doi.org/10.1016/j.physletb.2015.02.009.

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Hiptmair, Ralf, Lingxiao Li, Shipeng Mao, and Weiying Zheng. "A fully divergence-free finite element method for magnetohydrodynamic equations." Mathematical Models and Methods in Applied Sciences 28, no. 04 (April 2018): 659–95. http://dx.doi.org/10.1142/s0218202518500173.

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We propose a finite element method for the three-dimensional transient incompressible magnetohydrodynamic equations that ensures exactly divergence-free approximations of the velocity and the magnetic induction. We employ second-order semi-implicit timestepping, for which we rigorously establish an energy law and, as a consequence, unconditional stability. We prove unique solvability of the linear systems of equations to be solved in every timestep. For those we design an efficient preconditioner so that the number of preconditioned GMRES iterations is uniformly bounded with respect to the number of degrees of freedom. As both meshwidth and timestep size tend to zero, we prove that the discrete solutions converge to a weak solution of the continuous problem. Finally, by several numerical experiments, we confirm the predictions of the theory and demonstrate the efficiency of the preconditioner.
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Dissertations / Theses on the topic "Divergence-free method"

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Qin, Tong. "An exactly divergence-free finite element method for non-isothermal flow problems." Thesis, University of British Columbia, 2013. http://hdl.handle.net/2429/45013.

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In this thesis the exactly divergence-free finite element method developed by Cockburn, Scheotzau and Kanschat in [13] and [14] is studied. This method is first reviewed in the context of Stokes problem. An interior penalty discontinuous Galerkin approach is formulated and analysed in the unified framework established in [13], [14] and [37]. Then we extend the method to non-isothermal flow problems, in particular, to a generalised Boussinesq equation. Following the work by Ricardo, Scheotzau and Qin in [34], the method is formulated and the numerical analysis is reviewed. Numerical examples are implemented and presented, which verify the theoretical error estimates and the exactly divergence-free property.
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Wang, Xue. "Preconditioned solenoidal basis method for incompressible fluid flows." Texas A&M University, 2004. http://hdl.handle.net/1969.1/3295.

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This thesis presents a preconditioned solenoidal basis method to solve the algebraic system arising from the linearization and discretization of primitive variable formulations of Navier-Stokes equations for incompressible fluid flows. The system is restricted to a discrete divergence-free space which is constructed from the incompressibility constraint. This research work extends an earlier work on the solenoidal basis method for two-dimensional flows and three-dimensional flows that involved the construction of the solenoidal basis P using circulating flows or vortices on a uniform mesh. A localized algebraic scheme for constructing P is detailed using mixed finite elements on an unstructured mesh. A preconditioner which is motivated by the analysis of the reduced system is also presented. Benchmark simulations are conducted to analyze the performance of the proposed approach.
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Poletto, Ruggero. "Divergence free development of the synthetic eddy method in order to improve synthetic turbulence for embedded LES simulations." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/divergence-free-development-of-the-synthetic-eddy-method-in-order-to-improve-synthetic-turbulence-for-embedded-les-simulations(2f45de25-fa39-4be1-b18d-252a73a09999).html.

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In order to increase results accuracy and to provide some time-dependency to CFD results, embedded RANS/LES simulations are getting more and more interesting. In order to run these simulations accurate LES boundary conditions are required, not to affect the downstream results with a poor quality synthetic turbulence generation. Considering the currently developped methodologies, it is not possible to generate a divergence free turbulent flow which satisfy a non isotropic state of turbulence. The author started from the Synthetic Eddy Method (SEM) defined by Jarrin (2009), and defined a new shape function with the ability to satisfy continuity. The new methodology, named Divergence Free SEM (DFSEM), is able to reproduce almost any kind of turbulence anisotropy by using a special shape function and adapting the eddies intensities in order to match the Reynolds stress tensor rather than using the Lund coefficients, as most of the precursor methodologies did. Results comparisons against SEM and some other very popular synthetic turbulence models in some academic cases, proved that a reduce influence on the downstream flow was achieved. In most of the cases the friction coefficient Cf , used as a performance parameter, benefit by reducing the downstream developping zone by almost 50% in most cases, when compared against SEM. Another issue that has been tackled regards the unphysical pressure fluctuations present because of the synthetic turbulence, due to non perfectly constant mass-flow rate imposed in stochastic methodologies. The new methodology also showed an increased flexibility as it has been tested in embedded DDES simulation, by using the blending function to activate/deactivate it, and again it showed improved performances when compared against standard SEM.
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Estibals, Élise. "Modélisation MHD et simulation numérique par des méthodes volumes finis. Application aux plasmas de fusion." Thesis, Université Côte d'Azur (ComUE), 2017. http://www.theses.fr/2017AZUR4023/document.

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Ce travail traite de la modélisation des plasmas de fusion qui est ici abordée à l'aide d'un modèle Euler bi-températures et du modèle de la magnétohydrodynamique (MHD) idéale et résistive. Ces modèles sont tout d'abord établis à partir des équations de la MHD bi-fluide et nous montrons qu'ils correspondent à des régimes asymptotiques différents pour des plasmas faiblement ou fortement magnétisés. Nous décrivons ensuite les méthodes de volumes finis pour des maillages structurés et non-structurés qui ont été utilisées pour approcher les solutions de ces modèles. Pour les trois modèles mathématiques étudiés dans cette thèse, les méthodes numériques reposent sur des schémas de relaxation. Afin d'appliquer ces méthodes aux problèmes de fusion par confinement magnétique, nous décrivons comment modifier les méthodes de volumes finis pour les appliquer à des problèmes formulés en coordonnées cylindriques tout en gardant une formulation conservative forte des équations. Enfin nous étudions une stratégie pour maintenir la contrainte de divergence nulle du champ magnétique qui apparait dans les modèles MHD. Une série de cas tests numériques pour les trois modèles est présentée pour différentes géométries afin de valider les méthodes numériques proposées
This work deals with the modeling of fusion plasma which is discussed by using a bi-temperature Euler model and the ideal and resistive magnetohydrodynamic (MHD) ones. First, these models are established from the bi-fluid MHD equations and we show that they correspond to different asymptotic regimes for lowly or highly magnetized plasma. Next, we describe the finite volume methods for structured and non-structured meshes which have been used to approximate the solution of these models. For the three mathematical models studied in this thesis, the numerical methods are based on relaxation schemes. In order to apply those methods to magnetic confinement fusion problems, we explain how to modify the finite volume methods to apply it to problem given in cylindrical coordinates while keeping a strong conservative formulation. Finally, a strategy dealing with the divergence-free constraint of the magnetic field is studied. A set of numerical tests for the three models is presented for different geometries to validate the proposed numerical methods
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Sherif, Ahmed. "Compact High-Order Accurate Scheme for Laminar Incompressible Two-Phase Flows." Electronic Thesis or Diss., Ecole centrale de Nantes, 2023. http://www.theses.fr/2023ECDN0004.

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L'objectif de cette thèse est de développer une méthode précise d'ordre élevé pour résoudre le problème d'écoulementlaminaire incompressible à deux phases. Trois tâches principales sont à accomplir. Premièrement, la méthode doit être stable en énergie, ce qui signifie que la condition sans divergence de l'équation de Navier-Stokes incompressible est satisfaite partout dans le domaine de calcul. Deuxièmement, les discontinuités locales apparaissant dans le champ d'écoulement diphasique doivent être capturées avec précision. Troisièmement, l'interface matérielle entre les deux fluides doit être représentée avec précision à chaque pas de temps. Dans ce travail, une nouvelle méthode Hybridizable Discontinuous Galerkin (HDG) est utilisée pour la discrétisation spatiale. Cette méthode hybride qui appartient à la famille des méthodes DG-FEM satisfait la condition sans divergence en introduisant des variables de trace de vitesse et de pression du même ordre plus une approximation de vitesse et de pression adaptée à l'intérieur des éléments. Deplus, les concepts de FEM eXtended (X-FEM) sont utilisés pour approximer les discontinuités dans le champ d'écoulement en enrichissant l'approximation FEM standard dans les éléments où deux fluides existent. Enfin, l'interface du matériau en mouvement entre les deux fluides est capturée à l'aide de la méthode Level-Set
The objective of this thesis is to develop a high-order accurate method to solve the two-phase incompressible laminar flowproblem. Three main tasks are to be achieved. First, the method has to be energy-stable meaning that the divergence-free condition of the incompressible Navier-Stokes equation is satisfied everywhere in the computational domain. Second, the local discontinuities arising in the two-phase flow field have to be captured accurately. Third, the material interface betweenthe two fluids has to be represented accurately in each time step. In this work, a novel Hybridizable Discontinuous Galerkin (HDG) method is used for the spatial discretization. This hybrid method that belongs to the family of DG-FEM methods satisfies the divergence-free condition by introducing velocity and pressure trace variables of the same order plus a tailoredvelocity and pressure approximation inside the elements. Furthermore, the concepts of eXtended FEM (X-FEM) are used toapproximate discontinuities in the flow field by enriching the standard FEM approximation in elements where two fluids exist. Finally, the moving material interface between the twofluids is captured using the Level-Set method
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Schraeder, Daniela. "Analytically divergence-free discretization methods for Darcy's problem." Thesis, University of Sussex, 2010. http://sro.sussex.ac.uk/id/eprint/2327/.

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Radial basis functions are well known for their applications in scattered data approximation and interpolation. They can also be applied in collocation methods to solve partial differential equations. We develop and analyse a mesh-free discretization method for Darcy's problem. Our approximation scheme is based upon optimal recovery, which leads to a collocation scheme using divergence-free positive denite kernels. Besides producing analytically incompressible flow fields, our method can be of arbitrary order, works in arbitrary space dimension and for arbitrary geometries. Firstly we establish Darcy's problem. To introduce the scheme we review and study divergence-free and curl-free matrix-valued kernels and their reproducing kernel Hilbert spaces. After developing the scheme, we find the approximation error for smooth target functions and the optimal approximation orders. Furthermore, we develop Sobolev-type error estimates for target functions rougher than the approximating function and show that the approximation properties extend to those functions. To find these error estimates, we apply band-limited approximation. Finally, we illustrate the method with numerical examples.
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Birkevold, Jens. "Divergence-free Isogeometric Methods for Flow in Porous Media." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-19546.

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This thesis is focused on solving the Darcy flow problem using divergence-free isogeometric methods, and comparing these results to the ones obtained using traditional finite element methods with Taylor Hood elements. A short introduction to B-splines is given, and a chapter is also about using repeated knots in the knot vectors to obtain a discontinuous basis for the finite element method. This can be useful when dealing with varying permeabilities.
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Schroeder, Philipp W. [Verfasser], Gert [Akademischer Betreuer] Lube, Gert [Gutachter] Lube, Andreas [Gutachter] Dillmann, and Leo G. [Gutachter] Rebholz. "Robustness of High-Order Divergence-Free Finite Element Methods for Incompressible Computational Fluid Dynamics / Philipp W. Schroeder ; Gutachter: Gert, Lube; Andreas, Dillmann; Leo G., Rebholz ; Betreuer: Gert, Lube." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2019. http://d-nb.info/1180026489/34.

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"Properties of Divergence-Free Kernel Methods for Approximation and Solution of Partial Differential Equations." Doctoral diss., 2016. http://hdl.handle.net/2286/R.I.39449.

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abstract: Divergence-free vector field interpolants properties are explored on uniform and scattered nodes, and also their application to fluid flow problems. These interpolants may be applied to physical problems that require the approximant to have zero divergence, such as the velocity field in the incompressible Navier-Stokes equations and the magnetic and electric fields in the Maxwell's equations. In addition, the methods studied here are meshfree, and are suitable for problems defined on complex domains, where mesh generation is computationally expensive or inaccurate, or for problems where the data is only available at scattered locations. The contributions of this work include a detailed comparison between standard and divergence-free radial basis approximations, a study of the Lebesgue constants for divergence-free approximations and their dependence on node placement, and an investigation of the flat limit of divergence-free interpolants. Finally, numerical solvers for the incompressible Navier-Stokes equations in primitive variables are implemented using discretizations based on traditional and divergence-free kernels. The numerical results are compared to reference solutions obtained with a spectral method.
Dissertation/Thesis
Doctoral Dissertation Applied Mathematics 2016
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Schroeder, Philipp W. "Robustness of High-Order Divergence-Free Finite Element Methods for Incompressible Computational Fluid Dynamics." Doctoral thesis, 2019. http://hdl.handle.net/11858/00-1735-0000-002E-E5BC-8.

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Books on the topic "Divergence-free method"

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Mhuiris, Nessan Mac Giolla. The construction and use of divergence free vector expansions for incompressible fluid flow calculations. Hampton, Va: ICASE, 1986.

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Blaha, Stephen. The origin of the standard model: The genesis of four quark and lepton species, parity violation, the electro weak sector, color SU(3), three visible generations of fermions, and one generation of dark matter with dark energy ; Quantum theory of the third kind : a new type of divergence-free quantum field theory supporting a unified standard model of elementary particles and quantum gravity based on a new method in the calculus of variations. Auburn, NH: Pingree-Hill Publishing, 2006.

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Blaha, Stephen. Quantum Theory of the Third Kind: A New Type of Divergence-free Quantum Field Theory Supporting a Unified Standard Model of Elementary Particles and Quantum Gravity based on a New Method in the Calculus of Variations. 2nd ed. Pingree-Hill Publishing, 2005.

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The construction and use of divergence free vector expansions for incompressible fluid flow calculations: [final report]. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1986.

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Book chapters on the topic "Divergence-free method"

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Cuvelier, C., A. Segal, and A. A. van Steenhoven. "Divergence-free elements." In Finite Element Methods and Navier-Stokes Equations, 288–322. Dordrecht: Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-010-9333-0_9.

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Vorozhtsov, Evgenii V., and Vasily P. Shapeev. "A Divergence-Free Method for Solving the Incompressible Navier–Stokes Equations on Non-uniform Grids and Its Symbolic-Numeric Implementation." In Computer Algebra in Scientific Computing, 430–50. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-26831-2_28.

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Turek, Stefan. "Multigrid Techniques for Simple Discretely Divergence-free Finite Element Spaces." In Multigrid Methods IV, 321–32. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-8524-9_24.

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Harouna, Souleymane Kadri, and Valérie Perrier. "No-Slip and Free-Slip Divergence-Free Wavelets for the Simulation of Incompressible Viscous Flows." In Cartesian CFD Methods for Complex Applications, 37–65. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61761-5_3.

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Kaliyeva, Kulyash. "Energy Conservation Law for the Turbulent Motion in the Free Atmosphere." In Advances in Systems Analysis, Software Engineering, and High Performance Computing, 105–38. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-8823-0.ch003.

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This chapter presents convergent-divergent flow in the free atmosphere which is governed by the three dimensional Navier-Stokes equations and deals with the fundamental problem of fluid dynamics. Considering air movement under influence divergence and rotation were found the true dependencies between the velocity vector and the pressure distribution. Following the classical procedure by using rotor operator and a well-known formula of vector analysis were obtained the second kind nonlinear Volterra-Fredholm integral equations in a matrix form which contained only three components of the velocity vector. According to the theory of the matrix operators were defined the velocity components by the successive approximation method. According to the obtained balance equation for the pressure distribution were defined significant properties of the transient convergent-divergent flow which provide a description of the constitutive relationships between three physical quantities: the velocity vector, the external and internal forces, the pressure distribution.
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"Divergence-free biorthogonal wavelets." In Wavelet Analysis and Multiresolution Methods, 240–54. CRC Press, 2000. http://dx.doi.org/10.1201/9781482290066-15.

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"Divergence-Free Multiwavelets on Rectangular Domains." In Wavelet Analysis and Multiresolution Methods, 217–39. CRC Press, 2000. http://dx.doi.org/10.1201/9781482290066-14.

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Cockburn, Bernardo, Fengyan Li, and Chi-Wang Shu. "Discontinuous Galerkin methods for equations with divergence-free solutions." In Computational Fluid and Solid Mechanics 2003, 1900–1902. Elsevier, 2003. http://dx.doi.org/10.1016/b978-008044046-0.50465-6.

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COCKBURN, B., F. LI, and C. SHU. "Discontinuous Galerkin methods for equations with divergence-free solutionspreliminary results." In Computational Fluid and Solid Mechanics 2003, 1900–1902. Elsevier, 2003. http://dx.doi.org/10.1016/b978-008044046-0/50465-6.

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Ammari, Habib, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab. "Layer Potential Techniques." In Mathematical Methods in Elasticity Imaging. Princeton University Press, 2015. http://dx.doi.org/10.23943/princeton/9780691165318.003.0002.

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This chapter considers some well-known results on the solvability and layer potentials for static and time-harmonic elasticity equations. It first reviews commonly used function spaces before introducing equations of linear elasticity and decomposing the displacement field into the sum of an irrotational (curl-free) and a solenoidal (divergence-free) field using the Helmholtz decomposition theorem. It then discusses the radiation condition for the time-harmonic elastic waves, which is used to select the physical solution to exterior problems. It also describes the layer potentials associated with the operators of static and time-harmonic elasticity, along with their mapping properties, and proves decomposition formulas for the displacement fields. Finally, it derives the Helmholtz–Kirchhoff identities, analyzes Neumann and Dirichlet functions, and states a generalization of Meyer's theorem concerning the regularity of solutions to the equations of linear elasticity.
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Conference papers on the topic "Divergence-free method"

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Yang, Shunchuan, Zhizhang David Chen, Yiqiang Johnny Yu, and Sergey Ponomarenko. "A vector-based divergence-free meshless method." In 2014 16th International Symposium on Antenna Technology and Applied Electromagnetics (ANTEM). IEEE, 2014. http://dx.doi.org/10.1109/antem.2014.6887728.

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Thompson, Richard J., and Trevor M. Moeller. "Finite Volume Method for Divergence-free Solutions to Maxwell's Equations." In 47th AIAA Plasmadynamics and Lasers Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2016. http://dx.doi.org/10.2514/6.2016-3226.

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Kawai, Soshi. "High-order divergence-free method for compressible MHD with shock waves." In 44th AIAA Plasmadynamics and Lasers Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2013. http://dx.doi.org/10.2514/6.2013-2756.

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Poletto, R., Alistair Revell, Timothy J. Craft, and Nicolas Jarrin. "DIVERGENCE FREE SYNTHETIC EDDY METHOD FOR EMBEDDED LES INFLOW BOUNDARY CONDITIONS." In Seventh International Symposium on Turbulence and Shear Flow Phenomena. Connecticut: Begellhouse, 2011. http://dx.doi.org/10.1615/tsfp7.2040.

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Kroger, H., and Nikolai Kornev. "Generation of Artificial Scalar Fluctuations based on the Divergence-Free Turbulent Spot Method." In THMT-18. Turbulence Heat and Mass Transfer 9 Proceedings of the Ninth International Symposium On Turbulence Heat and Mass Transfer. Connecticut: Begellhouse, 2018. http://dx.doi.org/10.1615/thmt-18.1020.

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Shams, Sheyda, and Masoud Movahhedi. "Dispersive Divergence-Free Vector Meshless Method for Time-Domain Analysis of Frequency-Dependent Media." In 2020 IEEE Asia-Pacific Microwave Conference (APMC 2020). IEEE, 2020. http://dx.doi.org/10.1109/apmc47863.2020.9331486.

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Choudhary, Aniruddha, Christopher J. Roy, Jean-François Dietiker, Mehrdad Shahnam, and Rahul Garg. "Code Verification for Multiphase Flows Using the Method of Manufactured Solutions." In ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting collocated with the ASME 2014 12th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/fedsm2014-21608.

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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 computational fluid dynamics (CFD) code. In order to perform code verification, the Method of Manufactured Solutions (MMS) is a rigorous technique that can be used in the absence of exact solution to the problem. This work addresses major aspects of performing code verification for multiphase flow codes using the open-source, multiphase flow code MFIX which employs a staggered-grid and a modified SIMPLE-based algorithm. Code verification is performed 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. Currently, the algebraic gas-solid exchange terms are neglected as these can be tested via unit-testing. The no-slip wall, free-slip wall, and pressure outflow boundary conditions are verified for 2D and 3D flows. A newly-developed curl-based manufactured solution for 3D divergence free flows is introduced. Temporal order of accuracy during unsteady calculations is also assessed. Techniques are introduced to generate manufactured solutions that satisfy the divergence-free constraint during the verification of the incompressible governing equations. Manufactured solutions with constraints due to boundary conditions as well as due to divergence-free flow are derived in order to verify the boundary conditions. Use of staggered grid and SIMPLE-based algorithm for numerical computations in MFIX requires specific issues to be addressed while performing MMS-based code verification. Lessons learned during this code verification exercise are discussed.
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Sherif, A., M. Visonneau, G. Deng, and L. Eça. "Divergence-Free Extended Hybridizable Discontinuous Galerkin Method (X-HDG) For Laminar Incompressible Two-Phase Flow." In 10th International Conference on Adaptative Modeling and Simulation. CIMNE, 2021. http://dx.doi.org/10.23967/admos.2021.035.

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Papnourias, Konstantinos, and John Ekaterinaris. "Numerical solution of the Maxwell Equations With A High-Order Divergence Free Preserving DG Method." In 43rd AIAA Plasmadynamics and Lasers Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2012. http://dx.doi.org/10.2514/6.2012-3296.

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Muldoon, Frank, and Sumanta Acharya. "Mass Conservation in the Immersed Boundary Method." In ASME 2005 Fluids Engineering Division Summer Meeting. ASMEDC, 2005. http://dx.doi.org/10.1115/fedsm2005-77301.

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The immersed boundary approach for the modeling of complex geometries in incompressible flows is examined critically from the perspective of satisfying boundary conditions and mass conservation. The system of discretized equations for mass and momentum can be inconsistent if the real velocities are used in defining the forcing terms used to satisfy the boundary conditions. As a result, the velocity is generally not divergence free and the pressure at locations in the vicinity of the immersed boundary is not physical. However, the use of the pseudo velocities in defining the forcing (as frequently done when the governing equations are solved using a fractional step or projection method) combined with the use of the specified velocity on the immersed boundary is shown to result in a consistent set of equations which allows a divergence free velocity but, depending on the time step used to obtain a steady state solution, is shown to have an undesirable effect of allowing significant permeability of the immersed boundary. An improvement is shown if the pressure gradient is integrated in time using the Crank-Nicholson scheme instead of the backward Euler scheme. However, even with this improvement a significant reduction in the time step and hence increase in computational expense is still required for sufficient satisfaction of the boundary conditions.
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Reports on the topic "Divergence-free method"

1

Yogev, David, Ricardo Rosenbusch, Sharon Levisohn, and Eitan Rapoport. Molecular Pathogenesis of Mycoplasma bovis and Mycoplasma agalactiae and its Application in Diagnosis and Control. United States Department of Agriculture, April 2000. http://dx.doi.org/10.32747/2000.7573073.bard.

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Mycoplasma bovis and M. agalactiae are two phylogenetically related mycoplasmas which cause economically significant diseases in their respective bovine or small ruminant hosts. These organisms cause persistent asymptomatic infections that can result in severe outbreaks upon introduction of carrier animals into susceptible herds. Little is known about the mechanisms underlying mycoplasma-host interaction, variation in virulence, or of the factors enabling avoidance of the host immune system. In recent years it has become apparent that the ability of pathogenic microorganisms to rapidly alter surface antigenic structures and to fine tune their antigenicity, a phenomena called antigenic variation, is one of the most effective strategies used to escape immune destruction and to establish chronic infections. Our discovery of a novel genetic system, mediating antigenic variation in M. bovis (vsp) as well as in M. agalactiae (avg) served as a starting point for our proposal which included the following objectives: (i) Molecular and functional characterization of the variable surface lipoproteins (Vsp) system of M. bovis and comparison with the Vsp-counterpart in M. agalactiae (ii) Determination of the role of Vsp proteins in the survival of M. bovis when confronted by host defense factors, (iii) Assessment of Vsp-based genetic and antigenic typing of M. bovis and M. agalactiae for epidemiology of infection and (iv) Improvement of diagnostic tests for M. bovis and M. agalactiae based on the vsp-and vsp-analogous systems. We have carried out an extensive molecular characterization of the vsp system and unravelled the precise molecular mechanism responsible for the generation of surface antigenic variation in M. bovis. Our data clearly demonstrated that the two pathogenic mycoplasma species possess large gene families encoding variable lipoprotein antigens that apparently play an important role in immune evasion and in pathogen-host interaction during infection. Phase variable production of these antigens was found to be mediated by a novel molecular mechanism utilizing double site-specific DNA inversions via an intermediate vsp configuration. Studies in model systems indicate that phase variation of VspA is relevant in interaction between M. bovis and macrophages or monocytes, a crucial stage in pathogenesis. Using an ELISA test with captured VspA as an antigen, phase variation was shown to occur in vivo and under field conditions. Genomic rearrangements in the avg gene family of M. agalactiae were shown to occur in vivo and may well have a role in evasion of host defences and establishment of chronic infection. An epidemiological study indicated that patterns of vsp-related antigenic variation diverge rapidly in an M. bovis infected herd. Marked divergence was also found with avg-based genomic typing of M. agalactiae in chronically infected sheep. However, avg-genomic fingerprints were found to be relatively homogeneous in different animals during acute stages of an outbreak of Contagious Agalactiae, and differ between unrelated outbreaks. These data support the concept of vsp-based genomic typing but indicate the necessity for further refinement of the methodology. The molecular knowledge on these surface antigens and their encoding genes provides the basis for generating specific recombinant tools and serological methods for serodiagnosis and epidemiological purposes. Utilization of these methods in the field may allow differentiating acutely infected herds from chronic herds and disease-free herds. In addition the highly immunogenic nature of these lipoproteins may facilitate the design of protective vaccine against mycoplasma infections.
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