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Spectral p ‐multigrid discontinuous Galerkin solution of the Navier–Stokes equations
Author(s) -
Bassi F.,
Franchi.,
Ghidoni A.,
Rebay S.
Publication year - 2010
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2430
Subject(s) - multigrid method , inviscid flow , mathematics , euler equations , discontinuous galerkin method , navier–stokes equations , euler's formula , finite element method , spectral method , computational fluid dynamics , spectral element method , flow (mathematics) , galerkin method , compressibility , mathematical analysis , partial differential equation , geometry , classical mechanics , physics , mixed finite element method , mechanics , thermodynamics
Discontinuous Galerkin (DG) methods are very well suited for the construction of very high‐order approximations of the Euler and Navier–Stokes equations on unstructured and possibly nonconforming grids, but are rather demanding in terms of computational resources. In order to improve the computational efficiency of this class of methods, a high‐order spectral element DG approximation of the Navier–Stokes equations coupled with a p ‐multigrid solution strategy based on a semi‐implicit Runge–Kutta smoother is considered here. The effectiveness of the proposed approach in the solution of compressible shockless flow problems is demonstrated on 2D inviscid and viscous test cases by comparison with both a p ‐multigrid scheme with non‐spectral elements and a spectral element DG approach with an implicit time integration scheme. Copyright © 2010 John Wiley & Sons, Ltd.