# Thermodynamical Effects and High Resolution Methods for Compressible Fluid Flows

## TL;DR

This paper refines the GRP solver to incorporate thermodynamical effects into high resolution methods for compressible fluid flows, emphasizing the importance of thermodynamics in accurately resolving strong waves and demonstrating solver versatility.

## Contribution

The paper introduces a refined GRP solver that integrates thermodynamic variations and works with generic equations of state, enhancing high resolution numerical methods for compressible flows.

## Key findings

- Thermodynamic effects significantly influence wave resolution.
- The refined GRP solver effectively handles strong waves.
- The solver is versatile across different equations of state.

## Abstract

One of the fundamental differences of compressible fluid flows from incompressible fluid flows is the involvement of thermodynamics. This difference should be manifested in the design of numerical methods and seems often be neglected in addition that the entropy inequality, as a conceptual derivative, is taken into account to reflect irreversible processes and verified for some first order schemes. In this paper, we refine the GRP solver to illustrate how the thermodynamical variation is integrated into the design of high resolution methods for compressible fluid flows and demonstrate numerically the importance of thermodynamic effect in the resolution of strong waves. As a by-product, we show that the GRP solver works for generic equations of state, and is independent of technical arguments.