Fast solution of incompressible flow problems with two-level pressure approximation
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Pestana, Jennifer and Silvester, David J. (2024) Fast solution of incompressible flow problems with two-level pressure approximation. Numerische Mathematik, 156 (4). pp. 1579-1602. ISSN 0029-599X (https://doi.org/10.1007/s00211-024-01420-z)
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Abstract
This paper develops efficient preconditioned iterative solvers for incompressible flow problems discretised by an enriched Taylor-Hood mixed approximation, in which the usual pressure space is augmented by a piecewise constant pressure to ensure local mass conservation. This enrichment process causes over-specification of the pressure when the pressure space is defined by the union of standard Taylor-Hood basis functions and piecewise constant pressure basis functions, which complicates the design and implementation of efficient solvers for the resulting linear systems. We first describe the impact of this choice of pressure space specification on the matrices involved. Next, we show how to recover effective solvers for Stokes problems, with preconditioners based on the singular pressure mass matrix, and for Oseen systems arising from linearised Navier-Stokes equations, by using a two-stage pressure convection-diffusion strategy. The codes used to generate the numerical results are available online.
ORCID iDs
Pestana, Jennifer
ORCID: https://orcid.org/0000-0003-1527-3178 and Silvester, David J.;
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Item type: Article ID code: 89583 Dates: DateEvent1 August 2024Published17 June 2024Published Online25 May 2024AcceptedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 14 Jun 2024 09:45 Last modified: 12 Dec 2024 15:30 URI: https://strathprints.strath.ac.uk/id/eprint/89583