A fast multipole boundary element method for the three dimensional linear water wave-structure interaction problem with arbitrary bottom topography. (August 2020)

• Record Type: Journal Article
• Authors: Nokob, Mohamed Hariri; Yeung, Ronald W.
• Is Part Of: Engineering analysis with boundary elements. Volume 117(2020)
• Page Start: 232
• Page End: 241
• Publication Date: 2020-08
• Subjects: Wave structure interaction -- Free surface flows -- Fast multipole method; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2020.04.004
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: We present a numerical method that allows for the efficient solution of general linear water-wave problems with multiple arbitrarily shaped bodies and seabed geometry when the number of unknowns in the problem N is large. The problem domain is divided into an internal region that is modeled using a simple-source boundary integral equation and an outer domain of uniform water depth. The contribution of this work is in introducing an adpative fast-multipole method to the solution procedure, thereby changing the complexity of the problem from O ( N 3 ) (or O ( N 2 ) with iterative solvers) to O ( N ) when N is large. The memory requirements scale linearly with N as well. This methodology is needed when the number of bodies is large, when structures with complex shapes are modeled, or when the bottom topography for a problem varies considerably. We use the procedure developed to study the effects of topography over two case examples of floating bodies: 4 truncated vertical cylinders over a bottom protrusion, for which results indicate how variations in topography cause changes to wave loads on the bodies and a configuration of 16 cylinders (with N ~ 150, 000) and the effects of the variable ocean floor are again considered.