Universität zu Köln

Rueda-Ramirez, Andres M., Ferrer, Esteban, Kopriva, David A., Rubio, Gonzalo and Valero, Eusebio (2021). A statically condensed discontinuous Galerkin spectral element method on Gauss-Lobatto nodes for the compressible Navier-Stokes equations. J. Comput. Phys., 426. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 1090-2716

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Abstract

We present a static-condensation method for time-implicit discretizations of the Discontinuous Galerkin Spectral Element Method on Gauss-Lobatto points (GL-DGSEM). We show that, when solving the compressible Navier-Stokes equations, it is possible to reorganize the linear system that results from the implicit time-integration of the GL-DGSEM as a Schur complement problem, which can be efficiently solved using static condensation. The use of static condensation reduces the linear system size and improves the condition number of the system matrix, which translates into shorter computational times when using direct and iterative solvers. The statically condensed GL-DGSEM presented here can be applied to linear and nonlinear advection-diffusion partial differential equations in conservation form with the standard and the split-form variants of the DGSEM. To test it we solve the compressible Navier-Stokes equations with direct and Krylov subspace solvers, and we show for a selected problem that using the statically condensed GL-DGSEM leads to speed-ups of up to 200 when compared to the time-explicit GL-DGSEM, and speed-ups of up to three when compared with the time-implicit GL-DGSEM that solves the global system. The GL-DGSEM has gained increasing popularity in recent years because it satisfies the summation-by-parts property, which enables the construction of provably entropy stable schemes, and because it is computationally very efficient. In this paper, we show that the GL-DGSEM has an additional advantage: It can be statically condensed. (C) 2020 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Rueda-Ramirez, Andres M. UNSPECIFIED UNSPECIFIED UNSPECIFIED Ferrer, Esteban UNSPECIFIED UNSPECIFIED UNSPECIFIED Kopriva, David A. UNSPECIFIED UNSPECIFIED UNSPECIFIED Rubio, Gonzalo UNSPECIFIED UNSPECIFIED UNSPECIFIED Valero, Eusebio UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-590847
DOI:	10.1016/j.jcp.2020.109953
Journal or Publication Title:	J. Comput. Phys.
Volume:	426
Date:	2021
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Place of Publication:	SAN DIEGO
ISSN:	1090-2716
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language FINITE-DIFFERENCE FORMULATIONS; CFD METHODS; SCHEMES; ERRORS; FORM; SOLVER Multiple languages Computer Science, Interdisciplinary Applications; Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/59084