High-Order Accurate Entropy Stable Finite Difference Schemes for One- and Two-Dimensional Special Relativistic Hydrodynamics

High-Order Accurate Entropy Stable Finite Difference Schemes for One- and Two-Dimensional Special Relativistic Hydrodynamics

Year:    2020

Author:    Junming Duan, Huazhong Tang

Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 1 : pp. 1–29

Abstract

This paper develops the high-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamic equations. The schemes are built on the entropy conservative flux and the weighted essentially non-oscillatory (WENO) technique as well as explicit Runge-Kutta time discretization. The key is to technically construct the affordable entropy conservative flux of the semi-discrete second-order accurate entropy conservative schemes satisfying the semi-discrete entropy equality for the found convex entropy pair. As soon as the entropy conservative flux is derived, the dissipation term can be added to give the semi-discrete entropy stable schemes satisfying the semi-discrete entropy inequality with the given convex entropy function. The WENO reconstruction for the scaled entropy variables and the high-order explicit Runge-Kutta time discretization are implemented to obtain the fully-discrete high-order entropy stable schemes. Several numerical tests are conducted to validate the accuracy and the ability to capture discontinuities of our entropy stable schemes.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2019-0124

Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 1 : pp. 1–29

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    29

Keywords:    Entropy conservative scheme entropy stable scheme high order accuracy finite difference scheme special relativistic hydrodynamics.

Author Details

Junming Duan

Huazhong Tang

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