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Domain Decomposition Preconditioners for Discontinuous Galerkin Discretizations of Compressible Fluid Flows

Published online by Cambridge University Press:  28 May 2015

Stefano Giani  and
Paul Houston
Stefano Giani*
Affiliation:
School of Engineering and Computing Sciences, Durham University, South Road, Durham, DH1 3LE, UK
Paul Houston*
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK
*
Corresponding author.Email address:stefano.giani@durham.ac.uk
Corresponding author.Email address:Paul.Houston@nottingham.ac.uk
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Abstract

In this article we consider the application of Schwarz-type domain decomposition preconditioners to the discontinuous Galerkin finite element approximation of the compressible Navier-Stokes equations. To discretize this system of conservation laws, we exploit the (adjoint consistent) symmetric version of the interior penalty discontinuous Galerkin finite element method. To define the necessary coarse-level solver required for the definition of the proposed preconditioner, we exploit ideas from composite finite element methods, which allow for the definition of finite element schemes on general meshes consisting of polygonal (agglomerated) elements. The practical performance of the proposed preconditioner is demonstrated for a series of viscous test cases in both two- and three-dimensions.

Keywords

65F0865N1265N1565N30Composite finite element methodsdiscontinuous Galerkin methodsdomain decompositionSchwarz preconditionerscompressible fluid flows
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 7 , Issue 2 , May 2014 , pp. 123 - 148
Copyright
Copyright © Global Science Press Limited 2014

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