A general numerical method for the solution of gravity wave problems. Part 1: 2D steep gravity waves in shallow water

Abstract

AbstractIn this paper, 2D steep gravity waves in shallow water are used to introduce and examine a new kind of numerical method for the solution of non‐linear problems called the finite process method (FPM). On the basis of the velocity potential function and the FPM, a numerical method for 2D non‐linear gravity waves in shallow water is described which can be applied to solve 3D problems, e.g. the wave resistance of a ship moving in deep or shallow water. The convergence is examined and a comparison with the results of other authors is made.The FPM can successfully avoid the use of iterative methods and therefore can overcome the disadvantages and limitations of such methods. In contrast to iterative methods, the FPM is insensitive to the selection of the initial solution and the number of unknowns. The basic idea of the FPM can be used to solve other non‐linear problems. Its disadvantage is that much more CPU time is needed to obtain a sufficiently accurate result.