Solving free surface fluid flow problems by the minimal kinetic energy functional

In this paper a more accurate minimization technique, namely the minimal kinetic energy method, is developed and used to investigate the free surface fluid flow caused by an obstacle on the bottom of a channel whose exact shape and location are unknown a priori. The fluid flow is assumed to be two-dimensional, steady, inviscid, incompressible, irrotational and under the effect of the gravitational force. The minimization technique is based on the combination of the boundary integral method and the variational principle technique. This technique is extensively used in identifying unknown bottom surfaces. To illustrate this technique the free surface profile to be applied in the inverse analysis has been generated following a direct formulation when the solid bottom boundary possesses a double hump/double depression, a hump in front of a step, and a depression and a hump in front of a step. For all problems considered, the numerical results are in excellent agreement with the known analytical solution. In fact the computed profiles for both the bottom and free surfaces are graphically indistinguishable from the analytical results. Copyright (C) 2001 John Wiley & Sons, Ltd.