Stationary phase and practical numerical evaluation of ship waves in shallow water

• Published in: Journal of hydrodynamics. Series B Vol. 29; no. 5; pp. 817 - 824
• Main Author: 张晨亮;王金宝;朱怡;Francis Noblesse
• Format: Journal Article
• Language: English
• Published: Singapore Elsevier Ltd 01.10.2017; Springer Singapore; School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China%Marine Design and Research Institute of China, Shanghai 20011, China%School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China%School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China; Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China; Marine Design and Research Institute of China, Shanghai 20011, China
• Subjects: Engineering; Engineering Fluid Dynamics; fourier integral; Hydrology/Water Resources; Numerical and Computational Physics; numerical evaluation; Ship waves; Simulation; Special Column on 32nd IWWWFB; stationary phase; numerical evaluation; Ship waves; stationary phase; fourier integral
• ISSN: 1001-6058; 1878-0342
• DOI: 10.1016/S1001-6058(16)60793-X

A simple and highly-efficient method for numerically evaluating the waves created by a ship that travels at a constant speed in calm water, of large depth or of uniform depth, is given. The method, inspired by Kelvin＇s classical stationary-phase analysis, is suited for evaluating far-field as well as near-field waves. More generally, the method can be applied to a broad class of integrals with integrands that contain a rapidly oscillatory trigonometric function with a phase function whose first derivative（and possibly also higher derivatives） vanishes at one or several points, commonly called points of stationary phase, with the range of integration.