A fast integral equation method for the two-dimensional Navier-Stokes equations

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...

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Veröffentlicht in:Journal of computational physics 2020-05, Vol.409, p.109353, Article 109353
Hauptverfasser: af Klinteberg, Ludvig, Askham, Travis, Kropinski, Mary Catherine
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Sprache:eng
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Zusammenfassung: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. •First working integral equation-based Navier-Stokes solver for general geometries.•High order accuracy in space (10th) and time (4th).•Linear or nearly-linear scaling in the number of discretization nodes.•Software available in Julia.
ISSN:0021-9991
1090-2716
1090-2716
DOI:10.1016/j.jcp.2020.109353