Preventing spurious pressure oscillations in split convective form discretization for compressible flows

This paper addresses issues in split convective form discretization in terms of the physical property of the pressure equilibrium to achieve physically-consistent, stable, and non-dissipative shock-free compressible flow simulations. Discrete pressure- and velocity-evolution equations are derived by using existing split convective form discretization, such as used in kinetic energy preserving (KEP) and kinetic energy and entropy preserving (KEEP) schemes. This analysis reveals that the existing KEP and KEEP schemes do not maintain the physical property of the pressure equilibrium due to the discretization of the internal energy convective term. The analysis also directly leads to the proposed split convective form discretization of the internal-energy convective term that strictly satisfies the pressure equilibrium at the discrete level. By applying the proposed discretization of the internal energy convective term to the existing KEEP scheme, this study shows that it is possible to satisfy the pressure equilibrium numerically with maintaining excellent kinetic energy and entropy preservation property. In numerical tests, the proposed scheme shows a superior numerical stability property without spurious pressure oscillations.