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Solution of Stokes flow in complex nonsmooth 2D geometries via a linear-scaling high-order adaptive integral equation scheme.
- Source :
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Journal of Computational Physics . Jun2020, Vol. 410, pN.PAG-N.PAG. 1p. - Publication Year :
- 2020
-
Abstract
- • A spectrally-accurate close evaluation scheme for Stokes boundary integral operators. • Adaptive panel refinement for arbitrarily shaped boundaries. • Graded meshes to treat corners. • Example problems from microfluidic chip design and vascular network flows. 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00219991
- Volume :
- 410
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Physics
- Publication Type :
- Academic Journal
- Accession number :
- 142979108
- Full Text :
- https://doi.org/10.1016/j.jcp.2020.109361