Topology optimization of irregular flow domain by parametric level set method in unstructured mesh

Abstract

In this study, we present a novel method for the topology optimization of the irregular flow domain using a parametric level set method (PLSM). Some improvement was applied on the CS-RBFs (radial basis functions with compact support)-based PLSM to make it suitable for nonuniform mesh, expanding the range field of engineering application of the PLSM. The optimization problem is solved by a gradient-based algorithm with Stokes equations as state constraints, and the objective is set to minimize the power dissipation subject to the volume constraint of flow channels. A PLSM is introduced to avoid the direct solving of the Hamilton–Jacobi partial differential equation, which can have the potential to break through the restriction of relying on structured meshes because no finite difference scheme is required. Then, a self-adaption support radius approach is presented to allow the parametric level set to be evolved on the nonuniformed mesh, which can expand the application of the PLSM to more complicated engineering problems with irregular geometric shapes. A volume integration scheme is applied during the design sensitivity analysis to calculate the shape derivatives, allowing the nucleation of new holes. Numerical examples in two and three dimensions are provided to demonstrate the effectiveness of the proposed method.