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arXiv · 2110.10749

A domain decomposition solution of the Stokes-Darcy system in 3D based on boundary integrals

Svetlana Tlupova
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Abstract

A framework is developed for a robust and highly accurate numerical solution of the coupled Stokes-Darcy system in three dimensions. The domain decomposition method is based on a Dirichlet-Neumann type splitting of the interface conditions and solving separate Stokes and Darcy problems iteratively. Second kind boundary integral equations are formulated for each problem. The integral equations use a smoothing of the kernels that achieves high accuracy on the boundary, and a straightforward quadrature to discretize the integrals. Numerical results demonstrate the convergence, accuracy, and dependence on parameter values of the iterative solution for a problem of viscous flow around a porous sphere with a known analytical solution, as well as more general surfaces.

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BibTeXRIS

Svetlana Tlupova. 2021-10-20. A domain decomposition solution of the Stokes-Darcy system in 3D based on boundary integrals. https://doi.org/10.1016/j.jcp.2021.110824

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