Invariant-domain preserving IMEX schemes for the nonequilibrium Gray Radiation-Hydrodynamics equations Part I

TL;DR

This paper introduces an invariant-domain preserving IMEX scheme for the complex nonequilibrium gray radiation-hydrodynamics equations, ensuring consistency, conservation, and stability, serving as a foundation for higher-order methods.

Contribution

It presents a novel IMEX scheme that preserves invariant domains for radiation-hydrodynamics, with proofs of consistency and convergence, and a new equation splitting approach.

Findings

The scheme is consistent, conservative, and invariant-domain preserving.

Numerical tests confirm convergence and stability.

The method lays groundwork for higher-order accuracy implementations.

Abstract

In this work we introduce an implicit-explicit invariant-domain preserving approximation of the nonequilibrium gray radiation-hydrodynamics equations. A time and space approximation of the system is proposed using a novel split of the equations composed of three elementary subsystems, two hyperbolic and one parabolic. The approximation thus realized is proved to be consistent, conservative, invariant-domain preserving, and first-order accurate. The proposed method is a stepping stone for achieving higher-order accuracy in space and time in the forthcoming second part of this work. The method is numerically illustrated and shown to converge as advertised. This paper is dedicated to the memory of Peter Lax.