Constraints Preserving Lax-Wendroff Flux Reconstruction for Relativistic Hydrodynamics with General Equations of State
arXiv:2505.05128 · doi:10.1007/s10915-025-03092-9
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.
References in corpus (19)
- Sources of Relativistic Jets in the Galaxy
- An HLLC Riemann Solver for Relativistic Flows: I. Hydrodynamics
- The Piecewise Parabolic Method for Multidimensional Relativistic Fluid Dynamics
- THC: a new high-order finite-difference high-resolution shock-capturing code for special-relativistic hydrodynamics
- An efficient shock-capturing central-type scheme for multidimensional relativistic flows. I. Hydrodynamics
- GENESIS: A high-resolution code for 3D relativistic hydrodynamics
- RAM: A Relativistic Adaptive Mesh Refinement Hydrodynamics Code
- WHAM: A WENO-based general relativistic numerical scheme I: Hydrodynamics
- A Second Order Godunov Method for Multidimensional Relativistic Magnetohydrodynamics
- Equation of State in Numerical Relativistic Hydrodynamics
- High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics
- Discontinuous Galerkin methods for general-relativistic hydrodynamics: formulation and application to spherically symmetric spacetimes
- Assessment of a high-resolution central scheme for the solution of the relativistic hydrodynamics equations
- 3D Hydrodynamic Simulations of Relativistic Extragalactic Jets
- An Approximate Lax-Wendroff-Type Procedure for High Order Accurate Schemes for Hyperbolic Conservation Laws
- Physical-constraints-preserving central discontinuous Galerkin methods for special relativistic hydrodynamics with a general equation of state
- Implicit High-Order Flux Reconstruction Solver for High-Speed Compressible Flows
- Lax-Wendroff flux reconstruction method for hyperbolic conservation laws
- High-order finite-difference entropy stable schemes for two-fluid relativistic plasma flow equations