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

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.