Some continuous and discontinuous Galerkin methods and structure preservation for incompressible flows

Xi Chen, Yuwen Li, Corina Drapaca, John Cimbala

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper, we present consistent and inconsistent discontinuous Galerkin (dG) methods for incompressible Euler and Navier–Stokes equations with the kinematic pressure, Bernoulli function and EMAC function. Semi- and fully discrete energy stability of the proposed dG methods are proved in a unified fashion. Conservation of total energy, linear, and angular momentum is discussed with both central and upwind fluxes. Numerical experiments are presented to demonstrate our findings and compare our schemes with conventional schemes in the literature in both unsteady and steady problems. Numerical results show that global conservation of the physical quantities may not be enough to demonstrate the performance of the schemes, and our schemes are competitive and able to capture essential physical features in several benchmark problems.

Original languageEnglish (US)
Pages (from-to)2155-2174
Number of pages20
JournalInternational Journal for Numerical Methods in Fluids
Volume93
Issue number7
DOIs
StatePublished - Jul 2021

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics

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