Number 5 pp. 5 Boundary integral techniques provide a convenient way to study the evolution of an interface between inviscid liquids. Several studies have revealed that standard numerical approximations tend to lead to unstable methods, and various remedies have been introduced and tested. With the insight gained from our linear analysis, we propose a new method that is spectrally accurate and linearly stable. Further, the exact dispersion relation is obtained for all the available discrete modes.
Numerical tests suggest that the method is also stable in the nonlinear regime.
However, our method runs into difficulties generic to methods based on Lagrangian motion. The markers accumulate near a stagnation point on the interface, forcing us to use an ever decreasing time step in our explicit method. We introduce a redistribution of markers to overcome this difficulty. When we redistribute according to equal arclength, we find excellent agreement with a method based on preserving equal spacing in arclength. 65R20, 76C10 PII .