Green's function techniques for the solution of time-dependent potential flows with a free surface in a bounded domain. [QUAKE and TDIET

Abstract

Two numerical techniques are described for the computation of the boundary value of time-dependent potential flows in a bounded domain where part of the boundary is a free surface. The linearized free surface condition relates the normal derivative of the potential to time derivatives of the potential on the undisturbed free surface. It is assumed that on the fixed part of the boundary the normal derivative of the potential is a given function of time. The problem is formulated via Green's identity. The first technique, QUAKE, uses the classical time-dependent Green's function which satisfies the linearized free surface condition, and the boundary value of the potential is obtained as a solution of an integral equation. The second technique, TDIET, uses the time-independent fundamental solution of the Laplace equation and the boundary value of the potential is obtained as a solution to a differentio-integral equation.