Bound-preserving discontinuous Galerkin methods for relativistic hydrodynamics

In this paper, we develop discontinuous Galerkin (DG) methods to solve ideal special relativistic hydrodynamics (RHD). In RHD, the density and pressure are positive. Units are normalized so that the speed of light is c = 1. Therefore, the velocity of the fluid has magnitude less than 1. To construct physically relevant numerical approximations, we develop a bound-preserving limiter to the scheme, extending the idea in (X. Zhang and C.-W. Shu, Journal of Computational Physics, 229 (2010), 8918-8934). This limiter can preserve the physical bounds for the numerical solution while maintaining its designed high order accuracy. With this limiter, we can prove the L-stability of the numerical scheme. Numerical experiments are performed to demonstrate the good performance of the boundpreserving DG scheme.