Robust and accurate central algorithms for Multi-Component mixture equations with Stiffened gas EOS

TL;DR

This paper introduces simple, robust, and conservative central algorithms for simulating multi-component gaseous mixtures with stiffened gas EOS, ensuring accuracy and stability in flow simulations.

Contribution

It develops fully conservative central schemes using RICCA and MOVERS+ for multi-component mixtures with stiffened gas EOS, addressing pressure oscillations and positivity preservation.

Findings

Algorithms effectively suppress pressure oscillations.

Numerical schemes preserve positivity of mass fractions.

Validated robustness and accuracy across multiple test cases.

Abstract

Simple and robust algorithms are developed for compressible Euler equations with the stiffened gas equation of state (EOS), representing gaseous mixtures in thermal equilibrium and without chemical reactions. These algorithms use a fully conservative approach in finite volume framework for approximating the governing equations. Also, these algorithms used central schemes with controlled numerical diffusion for this purpose. Both Mass fraction (Y ) and $\gamma$ based models are used with RICCA and MOVERS+ algorithms to resolve the basic features of the flow fields. These numerical schemes are tested thoroughly for pressure oscillations and preservation of the positivity of mass fraction at least in the first-order numerical methods. Several test cases in both 1D and 2D are presented to demonstrate the robustness and accuracy of the numerical schemes.