Entropy-stable fluxes for high-order Discontinuous Galerkin simulations of high-enthalpy flows

TL;DR

This paper develops an entropy- and energy-preserving flux function for high-order Discontinuous Galerkin methods, enabling accurate simulation of high-enthalpy reacting gas flows with internal degrees of freedom.

Contribution

It introduces a novel flux function that preserves entropy and kinetic energy, extending DGSEM to complex high-enthalpy reacting flows.

Findings

The method accurately simulates high-enthalpy flows.

It compares favorably to the DLR TAU solver.

The flux function allows flexible internal energy expressions.

Abstract

In the present work, we extend the Discontinuous Galerkin Spectral Element Method (DGSEM) to high-enthalpy reacting gas flows with internal degrees of freedom. An entropy- and kinetic energy-preserving flux function is proposed which allows for use of arbitrary expressions for the internal energies of the constituent gas species. The developed method is applied to simulation of several model problems and compared to the DLR TAU solver.