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Kinetic Energy Preserving and Entropy Stable Finite Volume Schemes for Compressible Euler and Navier-Stokes Equations

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Communications in Computational Physics 2013年第10期14卷 1252-1286页

作者： praveen chandrashekar TIFR Center for Applicable Mathematics Bangalore 560065India

Centered numerical fluxes can be constructed for compressible Euler equations which preserve kinetic energy in the semi-discrete finite volume *** essential feature is that the momentum flux should be of the form ■ are any consistent approximations to the pressure and the mass *** scheme thus leaves most terms in the numerical flux unspecified and various authors have used simple *** we enforce approximate or exact entropy consistency which leads to a unique choice of all the terms in the numerical *** a consequence novel entropy conservative flux that also preserves kinetic energy for the semi-discrete finite volume scheme has been *** fluxes are centered and some dissipation has to be added if shocks are present or if the mesh is *** construct scalar artificial dissipation terms which are kinetic energy stable and satisfy approximate/exact entropy ***,we use entropy-variable based matrix dissipation flux which leads to kinetic energy and entropy stable *** schemes are shown to be free of entropy violating solutions unlike the original Roe *** hypersonic flows a blended scheme is proposed which gives carbuncle free solutions for blunt body *** results for Euler and Navier-Stokes equations are presented to demonstrate the performance of the different schemes.

关键词： Euler equation Navier-Stokes equation finite volumemethod kinetic energy preservation entropy conservation

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Single-Step Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for 1-D Euler Equations

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Communications on Applied Mathematics and Computation 2020年第4期2卷 541-579页

作者： Jayesh Badwaik praveen chandrashekar Christian Klingenberg Department of Mathematics University of WürzburgWürzburgGermany TIFR Center for Applicable Mathematics BangaloreIndia

We propose an explicit,single-step discontinuous Galerkin method on moving grids using the arbitrary Lagrangian-Eulerian approach for one-dimensional Euler *** grid is moved with the local fluid velocity modified by some smoothing,which is found to con-siderably reduce the numerical dissipation introduced by Riemann *** scheme preserves constant states for any mesh motion and we also study its positivity preservation *** grid refinement and coarsening are performed to maintain the mesh qual-ity and avoid the appearance of very small or large ***,higher order methods are developed and several test cases are provided to demonstrate the accuracy of the proposed scheme.

关键词： Discontinuous Galerkin method Moving meshes Arbitrary Lagrangian-Eulerian Euler equations

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