Computational Methods for Moving Interfaces using Boundary Integrals

at Berkeley intended to develop a numerical method for moving interfaces in viscous fluid. The interface exerts a force on the fluid; the force could be surface tension or the response of an elastic material. The immersed boundary method of C. Peskin was designed for this model and has been widely applied to biological problems. We have begun with the case of two-dimensional Stokes flow. In our approach, the jumps in pressure and velocity gradient at the interface lead to a representation of the velocity by layer potentials. With periodic boundary conditions, we use Ewald summation to write the boundary integral in a local part, approximated analytically, and a smooth part, computed as a Fourier series. The velocity can be found accurately on or off the interface. This approach is related to earlier work of both authors on computing singular or nearly singular integrals. The motion of the interface is found using the computed velocity and an adaptive level set method previously developed by Strain. 1 Qualitative properties for solutions of viscous fluid problems with anisotropic dissipatio