Abstract:

We present a level-set-based adaptive mesh method for solving the drag minimization problem of incompressible flow governed by the Stokes equations. A shape sensitivity analysis of the cost functional is presented. Two levels of meshes are employed during the optimization. A uniform coarse mesh for evolving the level set function is defined over the entire computational domain. Additionally, the level set function serves as a refinement indicator. The coarse mesh comprising the interfaces is then further divided into a uniform fine mesh. The computation is performed mainly near the interfaces. Therefore, the computational cost is significantly reduced compared with the uniform refined mesh over the whole domain that achieves the same resolution. Furthermore, the shape derivative on the boundary can be obtained implicitly, which is a very challenging task in classical optimal shape design problems.

Key words: adaptive mesh method, level set method, Stokes problem, shape optimization