Entropy stable discontinuous Galerkin schemes for the Relativistic Hydrodynamic Equations

2019/11/18 by Biswarup Biswas, Harish Kumar, Biswas, Biswarup +1
Earth and Planetary Sciences · Engineering · #Computational Fluid Dynamics and Aerodynamics #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1911.07488

openalex publication_date 2019/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Strong Stability-Preserving High-Order Time Discretization Methods

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