A positivity-preserving high-order weighted compact nonlinear scheme for compressible gas-liquid flows

We present a robust, highly accurate, and efficient positivity- boundedness-preserving diffuse interface method for the simulations of compressible gas-liquid two-phase flows with five-equation model by Allaire et al. using high-order finite difference weighted compact nonlinear scheme (WCNS) in explicit form. The equation states gas liquid are given ideal stiffened laws respectively. Under mild assumption on relative magnitude between ratios specific heats liquid, we can construct limiting procedures fifth order incremental-stencil WCNS (WCNS-IS) first Harten-Lax-van Leer contact (HLLC) flux such that positive partial densities squared speed sound be ensured solutions, together bounded volume fractions mass fractions. discretely conservative all equations also easily extended any other or scheme. Numerical tests water air reported to demonstrate robustness high accuracy WCNS-IS limiters even under extreme conditions.