Numerical experiments using high-resolution schemes for unsteady, inviscid, compressible flows

A. Bagabir, D. Drikakis

Research output: Contribution to journalArticle

43 Citations (Scopus)

Abstract

The performance of seven high-resolution schemes is investigated in various unsteady, inviscid, compressible flows. We employ the Roe, HLL (Harten, Lax and van Leer), and HLLC (Toro et al.) Riemann solvers, two variants of the van Leer and Steger–Warming flux vector splitting (FVS) schemes, Rusanov's scheme, and a hybrid total variation diminishing (TVD) scheme that combines a high-order Riemann solver with a flux vector splitting scheme. The above schemes have been implemented in conjunction with an implicit-unfactored method which is based on Newton-type sub-iterations and Gauss–Seidel relaxation. The performance of the schemes has been assessed in six unsteady flow problems: two one-dimensional shock tube problems, shock-wave reflection from a wedge, shock-wave diffraction around a cylinder, blast-wave propagation in an enclosure, and interaction of a shock wave with a gas bubble. More dissipative schemes do not necessarily provide faster convergence per time step and also suppress instabilities that occur in certain unsteady flow problems. The efficiency of the solution depends strongly on the advective (high-resolution) scheme. The results reveal that the Roe, HLLC and hybrid TVD schemes provide similar and overall the best results. For the unsteady problems considered here, the computations show that an explicit implementation based on a TVD, fourth-order Runge–Kutta method results in longer computing times than the implicit-unfactored method.
LanguageEnglish
Pages4675-4705
Number of pages31
JournalComputer Methods in Applied Mechanics and Engineering
Volume193
Issue number42-44
DOIs
Publication statusPublished - 22 Oct 2004

Fingerprint

compressible flow
Compressible flow
flux vector splitting
TVD schemes
Shock waves
shock waves
unsteady flow
Unsteady flow
trucks
high resolution
Fluxes
wave diffraction
Runge-Kutta method
wave reflection
Shock tubes
Runge Kutta methods
Experiments
shock tubes
blasts
enclosure

Keywords

  • high-resolution schemes
  • Godunov methods
  • implicit methods
  • explicit methods
  • compressible flows
  • shock waves
  • unsteady flows
  • instabilities

Cite this

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Numerical experiments using high-resolution schemes for unsteady, inviscid, compressible flows. / Bagabir, A.; Drikakis, D.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 193, No. 42-44, 22.10.2004, p. 4675-4705.

Research output: Contribution to journalArticle

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