On Optimum Profiles in Two-Dimensional Stokes Flow

Abstract

An inverse procedure for minimizing the hydrodynamic drag of a body is proposed. The distribution of optimum body-deformation vectors is determined in each iterative step by solving an integral equation. The method is applied to two-dimensional Stokes flow. The basic equations with boundary conditions are converted into a set of integral equations. For the inverse procedure, another integral equation is introduced to obtain the distribution of an optimum body-deformation vector. The final optimum shape with the volume specified is obtained by an iterative scheme. Other various restrictions for length, beam, and/or moments are also taken into account. Numerical results and discussions on the optimum shapes are made. The present method can be applied to other flows like Oseen flow, cavity flow, and boundary-layer flow, and wll even be applied to the problem of ship viscousresistance optimization.