Multigrid algorithms for high-order discontinuous Galerkin discretizations of the compressible Navier–Stokes equations

Multigrid algorithms are developed for systems arising from high-order discontinuous Galerkin discretizations of the compressible Navier–Stokes equations on unstructured meshes. The algorithms are based on coupling both p- and h-multigrid ( ph-multigrid) methods which are used in nonlinear or linear...

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Bibliographic Details
Published in:Journal of computational physics Vol. 228; no. 21; pp. 7917 - 7940
Main Authors: Shahbazi, Khosro, Mavriplis, Dimitri J., Burgess, Nicholas K.
Format: Journal Article
Language:English
Published: Kidlington Elsevier Inc 20.11.2009
Elsevier
Subjects:
Compressible Navier–Stokes equations
Computational techniques
Discontinuous Galerkin methods
Exact sciences and technology
High-order methods
Krylov subspace methods
Mathematical methods in physics
Multigrid methods
Physics
Preconditioning
Compressible Navier–Stokes equations
Discontinuous Galerkin methods
High-order methods
Multigrid methods
Krylov subspace methods
Preconditioning
Linear form
Calculation methods
Galerkin-Petrov method
Algorithms
Discretization
Laminar flow
Newton Krylov method
Multigrid
Convergence rate
Calculation
Performance
Navier-Stokes equations
Compressible Navier-Stokes equations
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:Multigrid algorithms are developed for systems arising from high-order discontinuous Galerkin discretizations of the compressible Navier–Stokes equations on unstructured meshes. The algorithms are based on coupling both p- and h-multigrid ( ph-multigrid) methods which are used in nonlinear or linear forms, and either directly as solvers or as preconditioners to a Newton–Krylov method. The performance of the algorithms are examined in solving the laminar flow over an airfoil configuration. It is shown that the choice of the cycling strategy is crucial in achieving efficient and scalable solvers. For the multigrid solvers, while the order-independent convergence rate is obtained with a proper cycle type, the mesh-independent performance is achieved only if the coarsest problem is solved to a sufficient accuracy. On the other hand, the multigrid preconditioned Newton–GMRES solver appears to be insensitive to this condition and mesh-independent convergence is achieved under the desirable condition that the coarsest problem is solved using a fixed number of multigrid cycles regardless of the size of the problem. It is concluded that the Newton–GMRES solver with the multigrid preconditioning yields the most efficient and robust algorithm among those studied.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2009.07.013