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

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Abstract

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.

Original languageEnglish
Article number110060
JournalJournal of Computational Physics
Volume427
DOIs
Publication statusPublished - 2021 Feb 15

Keywords

  • Compressible flows
  • Kinetic energy and entropy preservation
  • Pressure equilibrium
  • Split convective form discretization

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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