Fast solution of incompressible flow problems with two-level pressure approximation

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 logoORCID: https://orcid.org/0000-0003-1527-3178 and Silvester, David J.;
  • Item type:Article
    ID code:89583
    Dates:
    Date
    Event
    1 August 2024
    Published
    17 June 2024
    Published Online
    25 May 2024
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:14 Jun 2024 09:45
    Last modified:11 Nov 2024 14:20
    URI:https://strathprints.strath.ac.uk/id/eprint/89583
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