Material distribution resembled level set method for optimal shape design of Stokes flow

Abstract

Inspired by the work of Borrvall and Petersson [1], we propose a novel algorithm for optimal shape design problem of two-dimensional Stokes flow in order to minimize a given objective functional. The setting of the optimization problem is in the most general form, which makes this work a nontrivial extension of [1]. Borrowed idea of material distribution method from shape or topology optimization in solid mechanics, we employ an implicit coupled level set method to track the interface (boundary) of the fluid flow. Although our target application in this work is optimal shape design of Stokes flow, the proposed method can be generalized to solve other shape or topology optimization problems in fluid mechanics need no further additional effort. The promising features of the proposed algorithm are illustrated by two numerical examples.