Simple Central Algorithms for Capturing Contact-Discontinuity in Multi-Component Mixture Equations with Stiffened Gas Equation of State.

Abstract

This study introduces the creation of straightforward and reliable algorithms aimed at simulating compressible Euler equations featuring a stiffened gas equation of state (EOS). These algorithms are crafted to faithfully depict gaseous mixtures in thermal equilibrium, excluding chemical reactions. The methodology relies on a fully conservative approach within a finite volume framework, employing central schemes with controlled numerical diffusion. The RICCA and MOVERS+ algorithms implement two models, specifically Mass fraction (Y) and Mixture gamma $(\gamma)$ based models. These models adeptly capture the fundamental characteristics of flow fields. Rigorous testing of the numerical schemes ensures the minimization of pressure oscillations and the preservation of mass fraction positivity, especially in first-order numerical methods. A series of one-dimensional (1D) and two-dimensional (2D) test cases are presented to showcase the effectiveness and precision of the developed algorithms. These tests provide compelling evidence of the algorithms' resilience and accuracy in simulating the intended flow phenomena.