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	A new stabilizing technique for boundary integral methods for water waves
	Hou, TY ; Zhang, PW
	2001
关键词	boundary integral method stability water waves WELL-POSEDNESS VORTEX METHOD CONVERGENCE MOTION 2-D
英文摘要	Boundary integral methods to compute interfacial flows are very sensitive to numerical instabilities. A previous stability analysis by Beale, Hou and Lowengrub reveals that a very delicate balance among terms with singular 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 filtering at certain places of the discretization. While this filtering technique is effective for two-dimensional (2-D) periodic fluid interfaces, it does not apply to nonperiodic fluid interfaces. Moreover, using the filtering technique alone does not seem to be sufficient to stabilize 3-D fluid interfaces. Here we introduce a new stabilizing technique for boundary integral methods for water waves which applies to nonperiodic and 3-D interfaces. A stabilizing 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 modified 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 effect of various stabilizing terms is illustrated through careful numerical experiments.; Mathematics, Applied; SCI(E); 3; ARTICLE; 235; 951-976; 70
语种	英语
出处	SCI
出版者	mathematics of computation
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/389130]
专题	数学科学学院
推荐引用方式 GB/T 7714	Hou, TY,Zhang, PW. A new stabilizing technique for boundary integral methods for water waves. 2001-01-01.

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