A hybrid domain decomposition and multigrid method for the acceleration of compressible viscous flow calculations on unstructured triangular meshes

Victorita Dolean, Stéphane Lanteri

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper is concerned with the formulation and the evaluation of a hybrid solution method that makes use of domain decomposition and multigrid principles for the calculation of two-dimensional compressible viscous flows on unstructured triangular meshes. More precisely, a non-overlapping additive domain decomposition method is used to coordinate concurrent subdomain solutions with a multigrid method. This hybrid method is developed in the context of a flow solver for the Navier-Stokes equations which is based on a combined finite element/finite volume formulation on unstructured triangular meshes. Time integration of the resulting semi-discrete equations is performed using a linearized backward Euler implicit scheme. As a result, each pseudo time step requires the solution of a sparse linear system. In this study, a non-overlapping domain decomposition algorithm is used for advancing the solution at each implicit time step. Algebraically, the Schwarz algorithm is equivalent to a Jacobi iteration on a linear system whose matrix has a block structure. A substructuring technique can be applied to this matrix in order to obtain a fully implicit scheme in terms of interface unknowns. In the present approach, the interface unknowns are numerical fluxes. The interface system is solved by means of a full GMRES method. Here, the local system solves that are induced by matrix-vector products with the interface operator, are performed using a multigrid by volume agglomeration method. The resulting hybrid domain decomposition and multigrid solver is applied to the computation of several steady flows around a geometry of NACA0012 airfoil.

Original languageEnglish
Pages (from-to)287-304
Number of pages18
JournalInternational Journal of Computational Fluid Dynamics
Volume14
Issue number4
DOIs
Publication statusPublished - 1 Jan 2001

Keywords

  • domain decomposition method
  • finite elements
  • finite volumes
  • multigrid algorithm
  • Navier-Stokes equations
  • parallel computing
  • triangular meshes

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