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Construction of Mod...
Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations
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- Winters, Andrew Ross (författare)
- Linköpings universitet,Tekniska fakulteten,Tillämpad matematik,Mathematical Institute
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- Kopriva, David A (författare)
- The Florida State University, USA,Department of Mathematics
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- Gassner, Gregor J (författare)
- University of Cologne, Germany,Mathematical Institute
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- Hindenlang, Florian (författare)
- Max Planck Institute for Plasma Physics,Division for Numerical Methods in Plasma Physics
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(creator_code:org_t)
- 1
- 2021-01-05
- 2021
- Engelska.
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Ingår i: Efficient high-order discretizations for computational fluid dynamics. - Cham : Springer. - 9783030606107 ; , s. 117-196
- Relaterad länk:
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https://liu.diva-por... (primary) (Raw object)
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http://arxiv.org/pdf...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not perfect and there remain some issues. Concerning robustness, DG has undergone an extensive transformation over the past seven years into its modern form that provides statements on solution boundedness for linear and nonlinear problems. This chapter takes a constructive approach to introduce a modern incarnation of the DG spectral element method for the compressible Navier-Stokes equations in a three-dimensional curvilinear context. The groundwork of the numerical scheme comes from classic principles of spectral methods including polynomial approximations and Gauss-type quadratures. We identify aliasing as one underlying cause of the robustness issues for classical DG spectral methods. Removing said aliasing errors requires a particular differentiation matrix and careful discretization of the advective flux terms in the governing equations.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- Discontinuous Galerkin methods
- Computational physics and engineering
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