On the Construction of High-Order and Exact Pressure Equilibrium Schemes for Arbitrary Equations of State

Abstract

Typical fully conservative discretizations of the Euler compressible single or multi-component fluid equations governed by a real-fluid equation of state exhibit spurious pressure oscillations due to the nonlinearity of the thermodynamic relation between pressure, density, and internal energy. A fully conservative, pressure-equilibrium preserving method and a high-order, fully conservative, approximate pressure-equilibrium preserving method are presented. Both methods are general and can handle an arbitrary equation of state and arbitrary number of species. Unlike existing approaches to discretize the multi-component Euler equations, we do not introduce non conservative updates, overspecified equations, or design for a specific equation of state. The proposed methods are demonstrated on inviscid smooth interface advection problems governed by three equations of state: ideal-gas, stiffened-gas, and van der Waals where we show orders of magnitude reductions in spurious pressure oscillations compared to existing schemes.