Topology optimization of steady Navier–Stokes flow with body force

This paper presents the topology optimization of steady Navier–Stokes flows with body forces that influence the optimal shape and topology of fluid flows. Based on the implicit expression of the fluid flow with the level set method, an optimization problem is formulated and analyzed using the continuous adjoint method. The shape and topological sensitivities are computed based on the adjoint and asymptotic analysis of the optimization problem. In the optimization procedure, the level set surface is evolved based on the shape sensitivity and nucleated based on the topological sensitivity simultaneously. Three kinds of body forces that are commonly used in the design of fluid devices, i.e. constant, nonuniform, and solution-dependent body forces, are considered in the two-dimensional and three-dimensional numerical examples. Numerical results demonstrate that this method can effectively achieve the topology optimization of the Navier–Stokes flows with body forces.