An Efficient Numerical Method for Studying Interfacial Motion in Two-Dimensional Creeping Flows

✍ Scribed by M.C.A Kropinski

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 221 KB
• Volume: 171
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.2001.6787

✦ Synopsis

We present new methods for computing the motion of two-dimensional closed interfaces in a slow viscous flow. The interfacial velocity is found through the solution to an integral equation whose analytic formulation is based on complex-variable theory for the biharmonic equation. The numerical methods for solving the integral equations are spectrally accurate and employ a fast multipole-based iterative solution procedure, which requires only O(N ) operations where N is the number of nodes in the discretization of the interface. The interface is described spectrally, and we use evolution equations that preserve equal spacing in arclength of the marker points. A small-scale decomposition is performed to extract the dominant term in the evolution of the interface, and we show that this dominant term leads to a CFL-type stability constraint. When in an equal arclength frame, this term is linear and we show that implicit time-integration schemes that are explicit in Fourier space can be formulated. We verify this analysis through several numerical examples.