A fast computational method for potential flows in multiply connected coastal domains

Abstract

We present a fast and accurate numerical method for constructing incompressible, inviscid and irrotational flows in two-dimensional coastal domains, which are unbounded multiply connected domains above an infinitely long coastline boundary. In the numerical method, we utilize a numerical conformal mapping method based on a boundary integral equation with the generalized Neumann kernel in order to construct conformal mappings from coastal domains onto four of Koebe’s canonical domains. The numerical method is fast and accurate, since it just requires \(O((m+1)n\ln n)\) operations and it converges with \(O(e^{-cn})\) for coastal domains of connectivity \(m+1\), where \(n\) is the number of nodes in discretizing each smooth boundary component and \(c\) is a positive constant. With some examples, we also show that it is applicable to arbitrary coastal domains with high connectivity and complex geometry.