A Variational Level Set Method for Topology Optimization Problems in Navier-Stokes Flow

A novel algorithm for the topology optimization problem in fluid dynamics is presented, with the Navier-Stokes equations as state constraints, and the objective is to minimize the dissipated power of the fluid subject to a fluid volume constraint. Although belongs to the level set method, our algorithm does not capture the boundary explicitly as in the classical one, which is easy to implement. Topological sensitivity information is used to nucleate new holes and guarantee the stabilization. Computational efficiency of the algorithm is verified using two benchmark examples. The numerical results are consistent with those obtained in the existing literature.