Paper Info
Title
A new stabilizing technique for boundary integral methods for water waves
Abstract
Boundary integral methods to compute interfacial ows are very sensitive to numerical instabilities. A previous stability analysis by Beale, Hou and Lowengrub reveals that a very delicate balance among terms with singu- lar integrals and derivatives must be preserved at the discrete level in order to maintain numerical stability. Such balance can be preserved by applying suitable numerical ltering at certain places of the discretization. While this ltering technique is eective for two-dimensional (2-D) periodic uid inter- faces, it does not apply to nonperiodic uid interfaces. Moreover, using the ltering technique alone does not seem to be sucient to stabilize 3-D uid interfaces. Here we introduce a new stabilizing technique for boundary integral meth- ods for water waves which applies to nonperiodic and 3-D interfaces. A sta- bilizing term is added to the boundary integral method which exactly cancels the destabilizing term produced by the point vortex method approximation to the leading order. This modied boundary integral method still has the same order of accuracy as the point vortex method. A detailed stability analysis is presented for the point vortex method for 2-D water waves. The eect of various stabilizing terms is illustrated through careful numerical experiments.
Year
DOI
Venue
2001
10.1090/S0025-5718-00-01287-4
Mathematics of Computation
Keywords
Field
DocType
water waves.,boundary integral method,. boundary integral method,stability,water wave,water waves,numerical stability,stability analysis
Order of accuracy,Discretization,Boundary value problem,Singular integral,Mathematical analysis,Vortex,Dispersion (water waves),Initial value problem,Numerical stability,Mathematics
Journal
Volume
Issue
ISSN
70
235
0025-5718
Citations 
PageRank 
References 
0
0.34
1
Authors
2
Name
Order
Citations
PageRank
Y. Thomas Hou12040186.12
Zhang PW27817.87