Universität zu Köln

Laskowski, Wojciech, Rueda-Ramirez, Andres M., Rubio, Gonzalo ORCID: 0000-0002-6231-4801, Valero, Eusebio and Ferrer, Esteban ORCID: 0000-0003-1519-0444 (2020). Advantages of static condensation in implicit compressible Navier-Stokes DGSEM solvers. Comput. Fluids, 209. OXFORD: PERGAMON-ELSEVIER SCIENCE LTD. ISSN 1879-0747

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Abstract

We consider implicit time-marching schemes for the compressible Navier-Stokes equations, discretised using the Discontinuous Galerkin Spectral Element Method with Gauss-Lobatto nodal points (GL-DGSEM). We compare classic implicit strategies for the full Jacobian system to our recently developed static condensation technique for GL-DGSEM Rueda-Ramirez et al.(2019), A Statically Condensed Discontinuous Galerkin Spectral Element Method on Gauss-Lobatto Nodes for the Compressible Navier-Stokes Equations [1]. The Navier-Stokes system is linearised using a Newton-Raphson method and solved using an iterative preconditioned-GMRES solver. Both the full and statically condensed systems benefit from a Block-Jacobi preconditioner. We include theoretical estimates for the various costs involved (i.e. calculation of full and condensed Jacobians, factorising and inverting the preconditioners, GMRES steps and overall costs) to clarify the advantages of using static condensation in GL-DGSEM, for varying polynomial orders. These estimates are then examined for a steady three-dimensional manufactured solution problem and for an two-dimensional unsteady laminar flow over a NACA0012 airfoil. In all cases, we test the schemes for high polynomial orders, which range from 2 to 8 for a manufactured solution case and from 2 to 5 for the NACA0012 airfoil. The statically condensed system shows computational savings, which relate to the smaller system size and cheaper Block-Jacobi preconditioner with smaller blocks and better polynomial scaling, when compared to the preconditioned full Jacobian system (not condensed). The advantage of using static condensation is more noticeable for higher polynomial orders. (C) 2020 Elsevier Ltd. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Laskowski, Wojciech UNSPECIFIED UNSPECIFIED UNSPECIFIED Rueda-Ramirez, Andres M. UNSPECIFIED UNSPECIFIED UNSPECIFIED Rubio, Gonzalo UNSPECIFIED orcid.org/0000-0002-6231-4801 UNSPECIFIED Valero, Eusebio UNSPECIFIED UNSPECIFIED UNSPECIFIED Ferrer, Esteban UNSPECIFIED orcid.org/0000-0003-1519-0444 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-319162
DOI:	10.1016/j.compfluid.2020.104646
Journal or Publication Title:	Comput. Fluids
Volume:	209
Date:	2020
Publisher:	PERGAMON-ELSEVIER SCIENCE LTD
Place of Publication:	OXFORD
ISSN:	1879-0747
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language ORDER DISCONTINUOUS GALERKIN; ADAPTATION STRATEGIES; PRECONDITIONERS; TRUNCATION; PARALLEL; SPARSE; ERRORS Multiple languages Computer Science, Interdisciplinary Applications; Mechanics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/31916