A unified framework of continuous and discontinuous Galerkin methods for solving the incompressible Navier–Stokes equation

Xi Chen, Yuwen Li, Corina Drapaca, John Cimbala

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we propose a unified numerical framework for the time-dependent incompressible Navier–Stokes equation which yields the H1-, H(div)-conforming, and discontinuous Galerkin methods with the use of different viscous stress tensors and penalty terms for pressure robustness. Under minimum assumption on Galerkin spaces, the semi- and fully-discrete stability is proved when a family of implicit Runge–Kutta methods are used for time discretization. Furthermore, we present a unified discussion on the penalty term. Numerical experiments are presented to compare our schemes with classical schemes in the literature in both unsteady and steady situations. It turns out that our scheme is competitive when applied to well-known benchmark problems such as Taylor–Green vortex, Kovasznay flow, potential flow, lid driven cavity flow, and the flow around a cylinder.

Original languageEnglish (US)
Article number109799
JournalJournal of Computational Physics
Volume422
DOIs
StatePublished - Dec 1 2020

All Science Journal Classification (ASJC) codes

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

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