Solution to Viscous Flow Field Domain Optimization Problems : Approach by the Traction Method

Abstract

For solution of dissipation energy minimization problems in a steady-state viscous flow field domain we applied the traction method that was proposed as a solution to domain optimization problems including a variation-constrained boundary in elliptic boundary value problems. Comparing this method to the mathematical programming method directly using the shape gradient function we can easily apply this method to domain optimization problems including the variation-constrained natural boundary. Also, we can easily implement this method with general-purpose FEM programs or BEM programs. We show the successful results of two-dimensional Stokes flow problems of a bending channel and a channel in which an isolated body exists.