On spurious vortical structures

D. Drikakis, P.K. Smolarkiewicz

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

The paper investigates the formation of spurious vortical structures in incompressible flow simulations employing Godunov-type methods. The present work is motivated by the earlier studies of Brown and Minion (1995, J. Comput. Phys.122, 165 and 1997, J. Comput. Phys.138, 734) who demonstrated for a variety of numerical schemes (and for the upwind-biased methods in particular) that spurious vortices can occur in underresolved flow simulations. The aim of our work is threefold: (i) to identify deficiencies in various Godunov-type methods leading to spurious flow structures, (ii) to examine the numerical mechanisms responsible for these artifacts, and (iii) to propose modifications of Godunov-type methods in order to recover the correct solutions even under insufficient grid resolution. Our results reveal that the occurrence of spurious solutions depends strongly on the Godunov-type method employed. We show that in addition to the dissipation properties of a scheme—emphasized by Brown and Minion—there are other factors that can also contribute to numerical artifacts. These include a vortical instability arising from the numerical discretization of the advective terms in the primitive variable formulation of the Navier–Stokes equations, the balance of dissipation among the different discretized terms in a Godunov-type method, as well as order of accuracy of the interpolation used to discretize the wave-speed dependent term of the Godunov flux.
Original languageEnglish
Pages (from-to)309-325
Number of pages17
JournalJournal of Computational Physics
Volume172
Issue number1
DOIs
Publication statusPublished - 1 Dec 2001

Keywords

  • finite volume
  • Godunov-type methods
  • unsteady incompressible flows

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