Hierarchic multigrid iteration strategy for the discontinuous Galerkin solution of the steady Euler equations | Zendy

Hillewaert Koen | Zendy; Chevaugeon Nicolas | Zendy; Geuzaine Philippe | Zendy; Remacle JeanFrançois | Zendy

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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

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.

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