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

TL;DR

This paper introduces high-order, fully conservative pressure-equilibrium schemes for arbitrary equations of state, significantly reducing spurious pressure oscillations in multi-component fluid simulations.

Contribution

It presents novel, general methods that preserve pressure equilibrium without non-conservative updates, applicable to any equation of state and multiple species.

Findings

Order of magnitude reduction in pressure oscillations

Applicable to ideal-gas, stiffened-gas, and van der Waals equations

Demonstrated on inviscid interface advection problems

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.