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

Koen Hillewaert (1) , Nicolas Chevaugeon (2) , Philippe Geuzaine (1) , Jean-François Remacle (2)

1 Cenaero
2 UCL - Université Catholique de Louvain = Catholic University of Louvain

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.

Mots clés: Euler equations; quadrature free; multigrid; Newton-Krylov method; discontinuous Galerkin

Domaines: Mécanique [physics.med-ph]; Matériaux

Koen Hillewaert, Nicolas Chevaugeon, Philippe Geuzaine, Jean-François Remacle. Hierarchic multigrid iteration strategy for the discontinuous Galerkin solution of the steady Euler equations. International Journal for Numerical Methods in Fluids, 2006, 51 (9 10), pp.1157-1176. ⟨10.1002/fld.1135⟩. ⟨hal-01006922⟩