Bound Preserving Lax-Wendroff Flux Reconstruction Method for Special Relativistic Hydrodynamics

TL;DR

This paper introduces a high-order, flux reconstruction scheme for special relativistic hydrodynamics that preserves physical admissibility and effectively handles discontinuities, demonstrating robustness and efficiency across various test cases.

Contribution

A Jacobian-free LWFR scheme combined with a scaling limiter and discontinuity indicator for stable, accurate solutions in relativistic hydrodynamics.

Findings

The scheme achieves high accuracy in smooth regions.

It effectively controls oscillations near discontinuities.

Numerical tests confirm robustness and efficiency.

Abstract

Lax-Wendroff flux reconstruction (LWFR) schemes have high order of accuracy in both space and time despite having a single internal time step. Here, we design a Jacobian-free LWFR type scheme to solve the special relativistic hydrodynamics equations on Cartesian grids. We then blend the scheme with a first-order finite volume scheme to control the oscillations near discontinuities. We also use a scaling limiter to preserve the physical admissibility of the solution after ensuring the scheme is admissible in means. A particular focus is given to designing a discontinuity indicator model to detect the local non-smoothness in the solution of the highly non-linear relativistic hydrodynamics equations. Finally, we present numerical results for a wide range of test cases to show the robustness and efficiency of the proposed scheme.