Year: 2021
Author: Weiyi Wang, Zhijun Tan
Communications in Computational Physics, Vol. 30 (2021), Iss. 1 : pp. 227–254
Abstract
In this paper, a fairly simple 3D immersed interface method based on the CG-Uzawa type method and the level set representation of the interface is employed for solving three-dimensional Stokes flow with singular forces along the interface. The method is to apply the Taylor's expansions only along the normal direction and incorporate the jump conditions up to the second normal derivatives into the finite difference schemes. A second order geometric iteration algorithm is employed for computing orthogonal projections on the surface with third-order accuracy. The Stokes equations are discretized involving the correction terms on staggered grids and then solved by the conjugate gradient Uzawa type method. The major advantages of the present method are the special simplicity, the ability in handling the Dirichlet boundary conditions, and no need of the pressure boundary condition. The method can also preserve the volume conservation and the discrete divergence free condition very well. The numerical results show that the proposed method is second order accurate and efficient.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2020-0137
Communications in Computational Physics, Vol. 30 (2021), Iss. 1 : pp. 227–254
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: 3D immersed interface method CG-Uzawa method Stokes flow level set method staggered grids singular forces.