Preconditioning methods for discontinuous Galerkin solutions of the Navier-Stokes equations
type: Item
instance of: scholarly article
title: Preconditioning methods for discontinuous Galerkin solutions of the Navier-Stokes equations
zbMATH Open document ID: 1185.76812
author: Laslo T. Diosady
author: David L. Darmofal
published in: Journal of Computational Physics
publication date: 2009-06-18T00:00:00Z
review text: This paper develops a Newton-Krylov method for the solution of steady compressible Navier-Stokes equations by using a discontinuous Galerkin (DK) discretization on unstructured meshes. Steady-state solutions are obtained using Newton-Krylov approach, whereas the linear system at each iteration is solved by employing a restarted GMRES algorithm whose fast convergence is achieved by examining several different preconditioners. An element line-Jacobi preconditioner is presented which solves a block-tridiagonal system along lines of maximum coupling in the flow. An incomplete block-LU factorization (block-ILU(0)) is also presented as a preconditioner, where the factorization is performed using a reordering of elements based upon the lines of maximum coupling. The block-ILU(0) factorization is performed in-place, and a linearization is presented which reduces both the memory and CPU time over the traditional dual matrix storage format. Additionally, a linear \(p\)-multigrid preconditioner is considered, where block-Jacobi, line-Jacobi and block-ILU(0) are used as smoothers. This last preconditioner improves significantly convergence in terms of number of iterations and CPU time, compared to a single-level block-Jacobi or line-Jacobi preconditioner.
reviewed by: Titus Petrila
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 5566330
zbMATH Keywords: implicit solvers
zbMATH Keywords: GMRES
zbMATH Keywords: ILU factorization
zbMATH Keywords: in-place factorization
describes a project that uses: PETSc
MaRDI profile type: Publication
full work available at URL: j.jcp.2009.02.035
OpenAlex ID: W2160063850
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DOI: 10.1016/J.JCP.2009.02.035
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description: scientific article; zbMATH DE number 5566330