Title: Fully implicit adaptive method using discontinuous Galerkin finite elements for high speed flows

Authors: R. Becker; K. Gokpi; E. Schall; D. Trujillo

Addresses: Laboratoire de Mathématiques Appliquées (LMA), Université de Pau et des Pays de l'Adour (UPPA), PB 1155, 64010, Pau, France. ' Laboratoire des Sciences de l'Ingénieur Appliquées la Mécaniques et au génie Electrique (SIAME), Université de Pau et des Pays de l'Adour (UPPA), PB 1155, 64010, Pau, France. ' Laboratoire des Sciences de l'Ingénieur Appliquées la Mécaniques et au génie Electrique (SIAME), Université de Pau et des Pays de l'Adour (UPPA), PB 1155, 64010, Pau, France. ' Laboratoire de Mathématiques Appliquées (LMA), Université de Pau et des Pays de l'Adour (UPPA), PB 1155, 64010, Pau, France

Abstract: In this paper, we present automatic and effective mesh refinement techniques for discontinuous Galerkin finite elements methods (DGFEMs) applied to high speed inviscid flows, and based on the CONCHA finite element Library. CONCHA is a C++ software designed for the simulation of complex flow problems. The structure of its finite element library is described in this publication. It also provides different implicit methods for numerical resolution, a posteriori error estimation, and local mesh refinement. The refinement techniques presented are built on hierarchical non-conforming meshes. Then, two test cases of supersonic flows are studied in order to emphasise CONCHA's efficiency, robustness and flexibility. Perspectives as well as limitations of such refinement techniques are finally discussed.

Keywords: adaptive refinement methods; error estimators; discontinuous Galerkin finite elements methods; non-conforming mesh adaptation; time implicit scheme; Euler equations; compressible flow; aerodynamics; mesh refinement; finite element method; FEM; high speed flow; inviscid flow; complex flows; simulation.

DOI: 10.1504/IJAD.2012.049126

International Journal of Aerodynamics, 2012 Vol.2 No.2/3/4, pp.222 - 239

Published online: 31 Oct 2014 *

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