On spurious vortical structures

D. Drikakis, P.K. Smolarkiewicz

Research output: Contribution to journalArticle

39 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.
LanguageEnglish
Pages309-325
Number of pages17
JournalJournal of Computational Physics
Volume172
Issue number1
DOIs
Publication statusPublished - 1 Dec 2001

Fingerprint

Flow simulation
artifacts
dissipation
incompressible flow
Incompressible flow
Flow structure
Navier-Stokes equation
Navier Stokes equations
interpolation
Interpolation
Vortex flow
simulation
grids
occurrences
vortices
Fluxes
formulations

Keywords

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

Cite this

Drikakis, D. ; Smolarkiewicz, P.K. / On spurious vortical structures. In: Journal of Computational Physics. 2001 ; Vol. 172, No. 1. pp. 309-325.
@article{44b312ea2fe544ee99085d1b491c6d06,
title = "On spurious vortical structures",
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.",
keywords = "finite volume, Godunov-type methods, unsteady incompressible flows",
author = "D. Drikakis and P.K. Smolarkiewicz",
year = "2001",
month = "12",
day = "1",
doi = "10.1006/jcph.2001.6825",
language = "English",
volume = "172",
pages = "309--325",
journal = "Journal of Computational Physics",
issn = "0021-9991",
number = "1",

}

Drikakis, D & Smolarkiewicz, PK 2001, 'On spurious vortical structures' Journal of Computational Physics, vol. 172, no. 1, pp. 309-325. https://doi.org/10.1006/jcph.2001.6825

On spurious vortical structures. / Drikakis, D.; Smolarkiewicz, P.K.

In: Journal of Computational Physics, Vol. 172, No. 1, 01.12.2001, p. 309-325.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On spurious vortical structures

AU - Drikakis, D.

AU - Smolarkiewicz, P.K.

PY - 2001/12/1

Y1 - 2001/12/1

N2 - 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.

AB - 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.

KW - finite volume

KW - Godunov-type methods

KW - unsteady incompressible flows

UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0035455624&partnerID=40&md5=b514fa0c796253d75ef899eda88161ad

U2 - 10.1006/jcph.2001.6825

DO - 10.1006/jcph.2001.6825

M3 - Article

VL - 172

SP - 309

EP - 325

JO - Journal of Computational Physics

T2 - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 1

ER -