Approach for simulating gas-liquid-like flows under supercritical pressures using a high-order central differencing scheme

This study proposes an approach for simulations of cryogenic fluid mixing under supercritical pressures using high-order schemes. In this approach, we introduce a pressure evolution equation and consistently construct numerical diffusion terms to maintain the velocity and pressure equilibriums at fluid interfaces. The interfaces with high density and temperature ratio are successfully captured without the generation of spurious oscillations, while a high-order central differencing scheme resolves the flow fields. The present method preserves the mass and momentum conservation properties, while the poor energy conservation property is recognized. The one-dimensional single and multi-species interface advection and two-dimensional cryogenic jet mixing problems demonstrate the superiority and robustness of the present method over a conventional fully conservative method.