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A fast integral equation method for the two-dimensional Navier-Stokes equations
Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada.ORCID iD: 0000-0001-7425-8029
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, USA.ORCID iD: 0000-0001-6616-8162
Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada.
2020 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 409, p. 109353-109353, article id 109353Article in journal (Refereed) Published
Abstract [en]

The integral equation approach to partial differential equations (PDEs) provides significant advantages in the numerical solution of the incompressible Navier-Stokes equations. In particular, the divergence-free condition and boundary conditions are handled naturally, and the ill-conditioning caused by high order terms in the PDE is preconditioned analytically. Despite these advantages, the adoption of integral equation methods has been slow due to a number of difficulties in their implementation. This work describes a complete integral equation-based flow solver that builds on recently developed methods for singular quadrature and the solution of PDEs on complex domains, in combination with several more well-established numerical methods. We apply this solver to flow problems on a number of geometries, both simple and challenging, studying its convergence properties and computational performance. This serves as a demonstration that it is now relatively straightforward to develop a robust, efficient, and flexible Navier-Stokes solver, using integral equation methods.

Place, publisher, year, edition, pages
2020. Vol. 409, p. 109353-109353, article id 109353
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-65002DOI: 10.1016/j.jcp.2020.109353ISI: 000522726000004Scopus ID: 2-s2.0-85080100753OAI: oai:DiVA.org:mdh-65002DiVA, id: diva2:1818751
Funder
Knut and Alice Wallenberg FoundationAvailable from: 2023-12-12 Created: 2023-12-12 Last updated: 2024-01-24Bibliographically approved

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af Klinteberg, Ludvig

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