# Structure-preserving operators for thermal-nonequilibrium hydrodynamics

## TL;DR

This paper introduces a structure-preserving numerical scheme for radiation hydrodynamics that maintains energy conservation and accurately captures shock discontinuities by discretizing conservation laws with algebraic transformations.

## Contribution

The authors develop a novel discretization strategy that preserves the mathematical structure of conservation laws at the discrete level, ensuring physical fidelity in simulations.

## Key findings

- Global conservation errors are within round-off level.
- The scheme accurately reproduces shock jump conditions.
- Flexible to various numerical methods like central differences and Runge-Kutta.

## Abstract

Radiation hydrodynamics simulations based on the one-fluid two-temperature model may violate the law of energy conservation because the governing equations are expressed in a nonconservative formulation. Here, we maintain the important physical requirements by employing a strategy based on the key concept that the mathematical structures associated with the conservative and nonconservative equations are preserved, even at the discrete level. To this end, we discretize the conservation laws and transform them via exact algebraic operations. The proposed scheme maintains the global conservation errors within the round-off level. In addition, a numerical experiment concerning the shock tube problem suggests that the proposed scheme well agrees with the jump conditions at the discontinuities regulated by the Rankine-Hugoniot relationship. The generalized derivation allows us to employ arbitrary central difference, artificial dissipation, and Runge-Kutta methods.