Level Set Based-Topology Optimization in a Viscous Fluid under Oseen Approximation

摘要

This paper proposes a topology optimization method incorporating level set boundary expressions based on the concept on the phase field method, under the Oseen equilibrium equation, which we apply to a minimum flow friction problem. The Oseen equation is a simplified equilibrium equation in which the nonlinear term is replaced with a linear term of the Navier-Stokes equation, guaranteeing good convergence of the numerical solutions.Using a reaction-diffusion equation to update the level set function, we construct a new topology optimization method for the Oseen flow problem which is able to create new holes and maintain clear boundaries in the target structure during the optimization process. To demonstrate the usefulness of our method, we obtained optimized structures of a flow channel for an internal Oseen flow problem.Comparison of the optimized structures obtained using the Oseen equation with those obtained via the Stokes equation revealed that only the former provided appropriately different optimized structures in response to Reynolds number variation.