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

TL;DR

This paper introduces a high-order Lax-Wendroff flux reconstruction method for relativistic hydrodynamics with general equations of state, addressing conversion and admissibility issues, and validating with complex test cases.

Contribution

It develops a novel high-order scheme for relativistic hydrodynamics that accommodates various equations of state and ensures physical admissibility.

Findings

The scheme accurately handles strong discontinuities and high Lorentz factors.

It provides a reliable conversion method for conservative to primitive variables.

Validation confirms robustness in complex relativistic flow scenarios.

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 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.