A computational method for simulating transient motions of an incompressible inviscid fluid with a free surface

Abstract

Abstract A new numerical method has been developed for the analysis of unsteady free surface flow problems. The problem under consideration is formulated mathematically as a two‐dimensional non‐linear initial boundary value problem with unknown quantities of a velocity potential and a free surface profile. The basic equations are discretized spacewise with a boundary element method and timewise with a truncated forward‐time Taylor series. The key feature of the present paper lies in the method used to compute the time derivatives of the unknown quantities in the Taylor series. The use of the Taylor series expansion has enabled us to employ a variable time‐stepping method. The size of time increment is determined at each time step so that the remainders of the truncated Taylor series should be equal to a given small error limit. Such a variable time‐stepping technique has made a great contribution to numerically stable computations. A wave‐making problem in a two‐dimensional rectangular water tank has been analysed. The computational accuracy has been verified by comparing the present numerical results with available experimental data. Good agreement is obtained.