Constraints Preserving Lax-Wendroff Flux Reconstruction for Relativistic Hydrodynamics with General Equations of State

Abstract: In the realm of relativistic astrophysics, the ideal equation of state with a constant adiabatic index provides a poor approximation due to its inconsistency with relativistic kinetic theory. However, it is a common practice to use it for relativistic fluid flow equations due to its simplicity. Here we develop a high-order Lax-Wendroff flux reconstruction method on Cartesian grids for solving special relativistic hydrodynamics equations with several general equations of state available in the literature. We also study the conversion from conservative to primitive variables, which depends on the equation of state in use, and provide an alternative method of conversion when the existing approach does not succeed. For the admissibility of the solution, we blend the high-order method with a low-order method on sub-cells and prove its physical admissible property in the case of all the equations of state used here. Lastly, we validate the scheme by several test cases having strong discontinuities, large Lorentz factor, and low density or pressure in one and two dimensions.