Entropy stable discontinuous Galerkin schemes for the special relativistic hydrodynamics equations

Biswas, Biswarup; Kumar, Harish; Bhoriya, Deepak

doi:10.1016/j.camwa.2022.02.019

Cited by 6 publications

(2 citation statements)

References 96 publications

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“…Such works were successfully extended to the special relativistic magnetohydrodynamics (RMHD) in [48,49], where the importance of divergence-free fields in achieving PCP methods is shown. Recently, the entropy-stable schemes were also developed for the special RHD or RMHD equations [12,14,15,16,7,17]. Most of the above mentioned methods are built on the 1D Riemann solver, which is used to solve the local 1D Riemann problem at the cell interface by picking up flow variations that are orthogonal to the cell interface and then give the exact or approximate Riemann solution.…”

Section: Introductionmentioning

confidence: 99%

Genuinely multidimensional physical-constraints-preserving finite volume schemes for the special relativistic hydrodynamics

Liu¹,

Tang²

2023

Preprint

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This paper develops the genuinely multidimensional HLL Riemann solver for the twodimensional special relativistic hydrodynamic equations on Cartesian meshes and studies its physical-constraint-preserving (PCP) property. Based on the resulting HLL solver, the firstand high-order accurate PCP finite volume schemes are proposed. In the high-order scheme, the WENO reconstruction, the third-order accurate strong-stability-preserving time discretizations and the PCP flux limiter are used. Several numerical results are given to demonstrate the accuracy, performance and resolution of the shock waves etc. as well as the genuinely multi-dimensional wave structures of our PCP finite volume schemes.

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Section: Introductionmentioning

confidence: 99%

Genuinely multidimensional physical-constraints-preserving finite volume schemes for the special relativistic hydrodynamics

Liu¹,

Tang²

2023

Preprint

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“…Recently, several authors have developed entropy stable finite-difference scheme for non-relativistic fluids and plasma flows [15], [32], [33], [34]. For the relativistic fluids, Duan et.al [35], Biswas [36], and Bhoriya et.al [1] have proposed entropy stable schemes.…”

Section: Introductionmentioning

confidence: 99%

High-order finite-difference entropy stable schemes for two-fluid relativistic plasma flow equations

Bhoriya¹,

Kumar²,

Chandrashekar³

2022

Preprint

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In this article, we propose high-order finite-difference entropy stable schemes for the twofluid relativistic plasma flow equations. This is achieved by exploiting the structure of the equations, which consists of three independent flux components. The first two components describe the ion and electron flows, which are modeled using the relativistic hydrodynamics equation. The third component is Maxwell's equations, which are linear systems. The coupling of the ion and electron flows, and electromagnetic fields is via source terms only. Furthermore, we also show that the source terms do not affect the entropy evolution. To design semi-discrete entropy stable schemes, we extend the RHD entropy stable schemes in [1] to three dimensions. This is then coupled with entropy stable discretization of the Maxwell's equations. Finally, we use SSP-RK schemes to discretize in time. We also propose ARK-IMEX schemes to treat the stiff source terms; the resulting nonlinear set of algebraic equations is local (at each discretization point). These equations are solved using the Newton's Method, which results in an efficient method. The proposed schemes are then tested using various test problems to demonstrate their stability, accuracy and efficiency.

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Entropy Stable Discontinuous Galerkin Schemes for Two-Fluid Relativistic Plasma Flow Equations

Bhoriya,

Biswas,

Kumar

et al. 2023

J Sci Comput

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Entropy stable discontinuous Galerkin schemes for the special relativistic hydrodynamics equations

Cited by 6 publications

References 96 publications

Genuinely multidimensional physical-constraints-preserving finite volume schemes for the special relativistic hydrodynamics

Genuinely multidimensional physical-constraints-preserving finite volume schemes for the special relativistic hydrodynamics

High-order finite-difference entropy stable schemes for two-fluid relativistic plasma flow equations

Entropy Stable Discontinuous Galerkin Schemes for Two-Fluid Relativistic Plasma Flow Equations

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