Entropy stable discontinuous Galerkin schemes for the Relativistic Hydrodynamic Equations
Numerical Analysis
2020-07-07 v3 Numerical Analysis
Computational Physics
Abstract
In this article, we present entropy stable discontinuous Galerkin numerical schemes for equations of special relativistic hydrodynamics with the ideal equation of state. The numerical schemes use the summation by parts (SBP) property of Gauss-Lobatto quadrature rules. To achieve entropy stability for the scheme, we use two-point entropy conservative numerical flux inside the cells and a suitable entropy stable numerical flux at the cell interfaces. The resulting semi-discrete scheme is then shown to entropy stable. Time discretization is performed using SSP Runge-Kutta methods. Several numerical test cases are presented to validate the accuracy and stability of the proposed schemes.
Keywords
Cite
@article{arxiv.1911.07488,
title = {Entropy stable discontinuous Galerkin schemes for the Relativistic Hydrodynamic Equations},
author = {Biswarup Biswas and Harish Kumar},
journal= {arXiv preprint arXiv:1911.07488},
year = {2020}
}