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Solution of Stokes flow in complex nonsmooth 2D geometries via a linear-scaling high-order adaptive integral equation scheme. (English) Zbl 1436.65202
Summary: We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex – possibly nonsmooth – geometries in two dimensions. We apply the panel-based quadratures of Helsing and coworkers to evaluate to high accuracy the weakly-singular, hyper-singular, and super-singular integrals arising in the Nyström discretization, and also the near-singular integrals needed for flow and traction evaluation close to boundaries. The resulting linear system is solved iteratively via calls to a Stokes fast multipole method. We include an automatic algorithm to “panelize” a given geometry, and choose a panel order, which will efficiently approximate the density (and hence solution) to a user-prescribed tolerance. We show that this adaptive panel refinement procedure works well in practice even in the case of complex geometries with large number of corners, or close-to-touching smooth curves. In one example, for instance, a model 2D vascular network with 378 corners required less than 200K discretization points to obtain a 9-digit solution accuracy.
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
76D07 Stokes and related (Oseen, etc.) flows
76M15 Boundary element methods applied to problems in fluid mechanics
Full Text: DOI
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