A positivity-preserving and conservative high-order flux reconstruction method for the polyatomic Boltzmann–BGK equation

T. Dzanic, F. D. Witherden, L. Martinelli

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this work, we present a positivity-preserving high-order flux reconstruction method for the polyatomic Boltzmann–BGK equation augmented with a discrete velocity model that ensures the scheme is discretely conservative. Through modeling the internal degrees of freedom, the approach is further extended to polyatomic molecules and can encompass arbitrary constitutive laws. The approach is validated on a series of large-scale complex numerical experiments, ranging from shock-dominated flows computed on unstructured grids to direct numerical simulation of three-dimensional compressible turbulent flows, the latter of which is the first instance of such a flow computed by directly solving the Boltzmann equation. The results show the ability of the scheme to directly resolve shock structures without any ad hoc numerical shock capturing method and correctly approximate turbulent flow phenomena in a consistent manner with the hydrodynamic equations.

Original languageEnglish (US)
Article number112146
JournalJournal of Computational Physics
Volume486
DOIs
StatePublished - Aug 1 2023
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

Keywords

  • Boltzmann equation
  • Discontinuous spectral element method
  • High-order
  • Kinetic scheme
  • Polyatomic

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