On the analysis of conservation- and pressure-equilibrium-preserving schemes for compressible real-fluid simulations

We present a new conservation- and pressure-equilibrium-preserving scheme for compressible real-fluid simulations under supercritical pressures. It is known well that steep density gradients in compressible real-fluid simulations, such as cryogenic jet injection simulations in liquid rocket engines, may generate severe spurious pressure oscillations resulting in the failure of simulations. The proposed scheme maintains the conservation property of the governing equations while approximately satisfying the pressure equilibrium property using a pressure-equilibrium compatibility condition derived from the governing equations. The numerical flux of internal energy in the total energy equation is newly constructed so that the pressure-equilibrium compatibility condition is approximately satisfied at the discrete level. The proposed scheme can be combined flexibly with conventional upwind and central-flux schemes. We discuss the performance of the proposed scheme through one-dimensional advection, shock-tube, and two-dimensional jet injection problems under supercritical pressures using the compressible Euler equations and the Soave-Redlich-Kwong (SRK) equation of state.