Domain decomposition preconditioners for discontinuous Galerkin discretizations of compressible fluid flows

Giani, Stefano; Houston, Paul

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.

Citation

Giani, S., & Houston, P. (2014). Domain decomposition preconditioners for discontinuous Galerkin discretizations of compressible fluid flows. Numerical Mathematics, 7(2), https://doi.org/10.1017/S100489790000091X

• Journal Article Type: Article
• Publication Date: May 1, 2014
• Deposit Date: Aug 26, 2015
• Publicly Available Date: Aug 26, 2015
• Journal: Numerical Mathematics: Theory, Methods and Applications
• Electronic ISSN: 1004-8979
• Peer Reviewed: Peer Reviewed
• Volume: 7
• Issue: 2
• DOI: https://doi.org/10.1017/S100489790000091X
• Public URL: https://nottingham-repository.worktribe.com/output/995823
• Publisher URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9683854&fulltextType=RA&fileId=S100489790000091X
• Additional Information: First published in Numerical Mathematics: Theory, Methods, Mathematics in volume 7 issue 2, 2014, published by Global Science Press.