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

Hillewaert, Koen;Chevaugeon, Nicolas;Geuzaine, Philippe;Remacle, Jean-François
(2006) 13th International Conference on Finite Elements for Flow Problems — Location: Swansea(Wales) (4.April.2005)

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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 (c) 2005 John Wiley & Sons, Ltd.
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Hillewaert, K., Chevaugeon, N., Geuzaine, P., & Remacle, J.-F. (2006). Hierarchic multigrid iteration strategy for the discontinuous Galerkin solution of the steady Euler equations. International Journal for Numerical Methods in Fluids, 51(9-10), 1157-1176. https://doi.org/10.1002/fld.1135 (Original work published 2006)