A Spectrally Accurate Boundary Integral Method for Interfacial Velocities in Two-Dimensional Stokes Flow (Communications in Computational Physics, 2010)
We present a new numerical method for solving two-dimensional Stokesflow with deformable interfaces such as dynamics of suspended drops or bubbles.The method is based on a boundary integral formulation for the interfacial velocityand 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 areformulated in the tangent angle and arc-length coordinates and, to reduce the stiffnessof the evolution equation, the marker points are evenly distributed in arc-length bychoosing a proper tangential velocity along the interfaces. Examples of Stokes flowwith bubbles are provided to demonstrate the accuracy and effectiveness of the numericalmethod.