Summary: MATHEMATICS OF COMPUTATION
Volume 67, Number 221, January 1998, Pages 137--182
S 0025­5718(98)00911­9
CONVERGENCE OF A NON­STIFF BOUNDARY INTEGRAL
METHOD FOR INTERFACIAL FLOWS
WITH SURFACE TENSION
H ’
ECTOR D. CENICEROS AND THOMAS Y. HOU
Abstract. 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 di#cult 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 two­density fluid interfaces with surface tension is presented. The method
is based on a scheme introduced by Hou, Lowengrub and Shelley [ J. Comp.
Phys. 114 (1994), pp. 312--338] to remove the high order stability constraint
or sti#ness. Some numerical filtering is applied carefully at certain places in
the discretization to guarantee stability. The key of the proof is to identify

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara
Hou, Thomas Yizhao - Applied and Computational Mathematics Department, California Institute of Technology

Collections: Mathematics