Volume 8, Issue 4
A Spectrally Accurate Boundary Integral Method for Interfacial Velocities in Two-dimensional Stokes Flow

Xu Sun & Xiaofan Li

Commun. Comput. Phys., 8 (2010), pp. 933-946.

Published online: 2010-08

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  • Abstract

We present a new numerical method for solving two-dimensional Stokes flow with deformable interfaces such as dynamics of suspended drops or bubbles. The method is based on a boundary integral formulation for the interfacial velocity and is spectrally accurate in space. We analyze the singular behavior of the integrals (single-layer and double-layer integrals) appearing in the equations. The interfaces are formulated in the tangent angle and arc-length coordinates and, to reduce the stiffness of the evolution equation, the marker points are evenly distributed in arc-length by choosing a proper tangential velocity along the interfaces. Examples of Stokes flow with bubbles are provided to demonstrate the accuracy and effectiveness of the numerical method.

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@Article{CiCP-8-933, author = {Xu Sun and Xiaofan Li}, title = {A Spectrally Accurate Boundary Integral Method for Interfacial Velocities in Two-dimensional Stokes Flow}, journal = {Communications in Computational Physics}, year = {2010}, volume = {8}, number = {4}, pages = {933--946}, abstract = {

We present a new numerical method for solving two-dimensional Stokes flow with deformable interfaces such as dynamics of suspended drops or bubbles. The method is based on a boundary integral formulation for the interfacial velocity and is spectrally accurate in space. We analyze the singular behavior of the integrals (single-layer and double-layer integrals) appearing in the equations. The interfaces are formulated in the tangent angle and arc-length coordinates and, to reduce the stiffness of the evolution equation, the marker points are evenly distributed in arc-length by choosing a proper tangential velocity along the interfaces. Examples of Stokes flow with bubbles are provided to demonstrate the accuracy and effectiveness of the numerical method.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.190909.090310a}, url = {http://global-sci.org/intro/article_detail/cicp/7603.html} }
TY - JOUR T1 - A Spectrally Accurate Boundary Integral Method for Interfacial Velocities in Two-dimensional Stokes Flow AU - Xu Sun & Xiaofan Li JO - Communications in Computational Physics VL - 4 SP - 933 EP - 946 PY - 2010 DA - 2010/08 SN - 8 DO - http://dor.org/10.4208/cicp.190909.090310a UR - https://global-sci.org/intro/cicp/7603.html KW - AB -

We present a new numerical method for solving two-dimensional Stokes flow with deformable interfaces such as dynamics of suspended drops or bubbles. The method is based on a boundary integral formulation for the interfacial velocity and is spectrally accurate in space. We analyze the singular behavior of the integrals (single-layer and double-layer integrals) appearing in the equations. The interfaces are formulated in the tangent angle and arc-length coordinates and, to reduce the stiffness of the evolution equation, the marker points are evenly distributed in arc-length by choosing a proper tangential velocity along the interfaces. Examples of Stokes flow with bubbles are provided to demonstrate the accuracy and effectiveness of the numerical method.

Xu Sun & Xiaofan Li. (1970). A Spectrally Accurate Boundary Integral Method for Interfacial Velocities in Two-dimensional Stokes Flow. Communications in Computational Physics. 8 (4). 933-946. doi:10.4208/cicp.190909.090310a
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