Fluid topology optimization using quadtree-based scaled boundary finite element method

This paper presents a fluid topology optimization method utilizing a quadtree scaled boundary finite element method (SBFEM). The method aims to minimize energy dissipation during fluid flow by employing quadtree mesh refinement in the design domain, integrating both velocity and pressure fields. Finer meshes are used near the fluid-structure interface and coarser meshes elsewhere. By leveraging the Stokes control equations for incompressible viscous fluids, the scaled boundary finite element transformation addresses hanging node issues between different elements and simplifies numerical computations by eliminating the need to solve fundamental solutions within the domain. The density-based topology optimization method is then used to determine optimal channel layouts. This proposed method reduces the number of elements and degrees of freedom (DOFs) of design variables while enhancing numerical analysis accuracy. By testing a series of numerical examples, the proposed method can obtain consistent results as those of finite-element-method (FEM)-based topology optimization with shortened time, which demonstrates the accuracy and efficiency of the proposed method.