We present a topology optimization method for the Stokes problem under multiple flow cases by an improved level set method. In the framework of level set method, an implicit reinitialization approach is developed by deriving a new formula for the smoothing parameter in the conventional reinitialization equation. And a spline-free parameterization re-meshing method is adopted to overcome the convergence difficulty in flow analysis and guarantee the direct loading of the no-slip boundary condition. The topology optimization method developed in this paper is used to implement the optimal design for Stokes flow with the different boundary conditions. Numerical examples demonstrate that the proposed approach is effective and robust for the topology optimization of Stokes problem under multiple flow cases.

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