Stability of boundary integral methods for water waves

Journal Article

This paper studies the numerical stability of method of boundary integral type, in which the free surface is tracked explicitly. The focus is on two-dimensional motions, periodic in the horizontal direction, so that issues of boundary conditions for the free surface can be avoided. The case considered is rather special, but analysis has provided a definitive answer in this case, and the treatment of this case might partially clarify the numerical issues in the more realistic problems. The results are presented in detail. A calculation of an overturning wave illustrates the resolution made possible by a fully stable numerical method. A careful study of an overturning wave by method of this class was presented previously.

Duke Authors

Cited Authors

  • Beale, JT; Hou, TY; Lowengrub, J

Published Date

  • 1996

Published In

  • AMS-IMS-SIAM Joint Summer Research Conference

Start / End Page

  • 241 - 245