A family of bound-preserving velocity-consistent schemes for two-medium γ-based model with stiffened gas

This study introduces a family of first-, second-, and fifth-order velocity-consistent (VC) schemes for simulating compressible two-medium flows, tailored explicitly for stiffened gas equations of state. The higher-order spatial discretizations employ a central upwind finite volume method with a minmod limiter (second-order) and an affine-invariant alternative WENO scheme (fifth-order). A key innovation is stabilizing the numerical diffusion coefficient within the global Lax-Friedrichs (LF) flux, which is typically a sensitive nonlinear function of the local Mach number and gas stiffness. This stabilization enables robust and consistent larger time steps when used with explicit third-order TVD-Runge-Kutta methods, significantly improving computational efficiency without sacrificing stability. Furthermore, the proposed VC schemes preserve velocity and pressure equilibrium (EP property) across material interfaces, ensuring accurate and oscillation-free solutions. To maintain physical admissibility, a hybrid flux-based bound-preserving (BP) limiter is integrated, judiciously blending high-order fluxes for accuracy with first-order VC fluxes for robustness. Extensive one-, two-, and three-dimensional numerical experiments validate the schemes’ ability to deliver stable, accurate, and bound-preserving solutions for challenging two-medium flow problems, even under extreme conditions.