Convergence of a non-stiff boundary integral method for interfacial flows with surface tension

@article{Ceniceros1998ConvergenceOA,
title={Convergence of a non-stiff boundary integral method for interfacial flows with surface tension},
author={H{\'e}ctor D. Ceniceros and Thomas Y. Hou},
journal={Math. Comput.},
year={1998},
volume={67},
pages={137-182}
}

Boundary integral methods to simulate interfacial flows are very sensitive to numerical instabilities. In addition, surface tension introduces nonlinear terms with high order spatial derivatives into the interface dynamics. This makes the spatial discretization even more difficult and, at the same time, imposes a severe time step constraint for stable explicit time integration methods. A proof of the convergence of a reformulated boundary integral method for two-density fluid interfaces with… CONTINUE READING