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


A Spectrally Accurate Boundary Integral Method for Interfacial Velocities in Two-Dimensional Stokes Flow

Xu Sun 1, Xiaofan Li 1*

1 Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA.

Received 19 September 2009; Accepted (in revised version) 9 March 2010
Available online 17 May 2010
doi:10.4208/cicp.190909.090310a

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.

AMS subject classifications: 45F15, 65R20, 76T10

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Key words: Boundary integral method, Stokes flow, two-phase flow, weakly singular integral, spectral accuracy.

*Corresponding author.
Email: xsun15@iit.edu (X. Sun), lix@iit.edu (X. Li)
 

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