A density-based topology optimization framework for steady Navier-Stokes flow with design-dependent wall actuation

Abstract

Design-dependent wall velocities are difficult to treat in density-based fluid topology optimization. This difficulty arises because the fluid-solid interface is represented implicitly and evolves with the design. This paper proposes a diffuse-interface formulation for topology optimization of steady incompressible Navier-Stokes flows with design-dependent wall actuation. A continuous topological description field parameterized by compactly supported radial basis functions (CS-RBFs) provides the local interface orientation, and its regularized projection defines the pseudo-density for Brinkman flow analysis. The wall velocity is imposed on a fixed mesh through an equivalent volumetric momentum source, which is localized by a diffuse-interface measure constructed from the pseudo-density and the gradient of the description field. Assuming a locally planar interface and uniformly distributed Wendland radial basis functions, the source coefficient is determined analytically by balancing the equivalent momentum input with the Brinkman resistance at the interface center. These assumptions also yield a characteristic transition-width estimate in terms of the projection steepness and support radius. Continuous adjoint analysis is performed to derive the design sensitivities. Two- and three-dimensional examples formulated using the analogy equation demonstrate the effectiveness of the proposed topology optimization method for flow-rate maximization. Body-fitted re-simulations verify the flow fields and transport performance of the optimized designs. The formulation is further extended to electroosmotic transport under the thin electric double layer (EDL) assumption using the Helmholtz-Smoluchowski relation.