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Hierarchic multigrid iteration strategy for the discontinuous Galerkin solution of the steady Euler equations
Author(s) -
Hillewaert Koen,
Chevaugeon Nicolas,
Geuzaine Philippe,
Remacle JeanFrançois
Publication year - 2005
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.1135
Subject(s) - multigrid method , quadrature (astronomy) , computation , finite element method , backward euler method , mathematics , euler equations , euler's formula , galerkin method , interpolation (computer graphics) , discontinuous galerkin method , euler method , boundary value problem , adaptive quadrature , computational fluid dynamics , boundary element method , mathematical optimization , computer science , partial differential equation , mathematical analysis , algorithm , control theory (sociology) , physics , animation , computer graphics (images) , control (management) , artificial intelligence , mechanics , optics , thermodynamics
Abstract We study the efficient use of the discontinuous Galerkin finite element method for the computation of steady solutions of the Euler equations. In particular, we look into a few methods to enhance computational efficiency. In this context we discuss the applicability of two algorithmical simplifications that decrease the computation time associated to quadrature. A simplified version of the quadrature free implementation applicable to general equations of state, and a simplified curved boundary treatment are investigated. We as well investigate two efficient iteration techniques, namely the classical Newton–Krylov method used in computational fluid dynamics codes, and a variant of the multigrid method which uses interpolation orders rather than coarser tesselations to define the auxiliary coarser levels. Copyright © 2005 John Wiley & Sons, Ltd.