An Entropy-Stable/Double-Flux scheme for the multi-component compressible Navier-Stokes equations

TL;DR

This paper introduces an entropy-stable, double-flux numerical scheme for multi-component compressible Navier-Stokes equations, enhancing stability, accuracy, and robustness in high-fidelity supersonic flow simulations.

Contribution

It develops a novel entropy-stable formulation combined with a double-flux scheme and hybrid dissipation, ensuring thermodynamic consistency and improved numerical stability.

Findings

Demonstrates low-dissipation, oscillation-free solutions.

Ensures the numerical flux satisfies a semi-discrete entropy inequality.

Validates the method with benchmark multi-dimensional flow cases.

Abstract

We present a novel combination of numerical techniques to improve the efficiency, accuracy, and robustness of multi-component compressible flow simulations. At the core of our approach is an Entropy-Stable formulation that preserves kinetic energy and integrates a Double-Flux scheme tailored for multi-component flows with variable specific heat ratios. This formulation yields low-dissipation, oscillation-free solutions and enhances stability compared to standard fully conservative methods. To further improve robustness, we introduce a new hybrid dissipation strategy that blends the Entropy-Stable/Double-Flux approach with conventional dissipation mechanisms. We provide a rigorous proof that the resulting numerical flux satisfies a semi-discrete entropy inequality, ensuring consistency with the second law of thermodynamics. For time integration, we employ an explicit Runge-Kutta scheme in combination with adaptive mesh refinement to capture local flow features dynamically. The method is implemented within an existing compressible Navier-Stokes solver based on OpenFOAM. Benchmark cases, including multi-dimensional interface and shock-interface interactions, demonstrate the effectiveness of the proposed framework. The results confirm its favorable stability and robustness, validating the approach as a promising advancement for high-fidelity simulations of supersonic flows.