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

Abstract

SUMMARYIn 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.

Flow domain identification from free surface velocity in thin inertial films

“…Furthermore, Heining (2011) proposed an iterative numerical scheme to solve the inverse problem for the full Navier-Stokes equation and a given free surface shape. We note that similar inverse problems were solved by Lonyangapuo et al (1999Lonyangapuo et al ( , 2001 but for inviscid and irrotational flows.…”

Modeling Open Channel Flows of a Viscous Fluid: Critical Transition and Apparent Bottom

“…The indirect problem can be solved using minimization techniques which are able to predict all the different shapes and positions of the bottom and solve iteratively the system with the boundary integral method. This is the basis of the minimal high method [32,33], the extremal pressure method [34,35], the extremal energy method [36], and the minimal kinetic energy method [37].…”