An edge based stabilized finite element method for solving compressible flows: Formulation and parallel implementation

Azzeddine Soulaimani, Yousef Saad, Ali Rebaine

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


This paper presents a finite element formulation for solving multidimensional compressible flows. This method is inspired by our experience with the SUPG, finite volume (FV) and discontinuous-Galerkin (DG) methods. Our objective is to obtain a stable and accurate finite element formulation for multi-dimensional hyperbolic-parabolic problems with particular emphasis on compressible flows. In the proposed formulation, the upwinding effect is introduced by considering the flow characteristics along the normal vectors to the element interfaces. This method is applied for solving inviscid, laminar and turbulent flows. The one-equation turbulence closure model of Spalart-Allmaras (S-A) is used. Several numerical tests are carried out, and a selection of two- and three-dimensional experiments is presented. The results are encouraging, and it is expected that more numerical experiments and theoretical analysis will lead to a greater insight into this formulation. We also discuss algorithmic and parallel implementation issues.

Original languageEnglish (US)
Pages (from-to)6735-6761
Number of pages27
JournalComputer Methods in Applied Mechanics and Engineering
Issue number49-50
StatePublished - Oct 12 2001

Bibliographical note

Funding Information:
This research has been funded by the Natural Sciences and Engineering Research Council of Canada (NSERC), PSIR research program of ETS and by la Fondation Bombardier. The second author acknowledges support from the National Science Foundation and from the Minnesota Supercomputer Institute. The authors would like to thank Prof. Bruno Koobus (Universite de Montpellier) for providing the results obtained with his FV code and Alexandre Forest for his help in generating the three-dimensional meshes.

Copyright 2007 Elsevier B.V., All rights reserved.


  • Compressible flows
  • Finite element method
  • Iterative methods
  • Parallel computing
  • Upwinding
  • Wings


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