Topology Optimization of Transient Two‐Phase Flows via Phase‐Field‐Based Penalty Interpolation Model

ABSTRACT Based on the characteristics of transient two‐phase flows, a novel phase‐field‐based penalty interpolation model is proposed in this study. The governing equations are established by coupling the Cahn–Hilliard phase‐field model with the Navier–Stokes–Brinkman equations. The numerical solution of the flow fields is computed using the streamline‐upwind Petrov–Galerkin stabilization method combined with the penalty finite element method, while the phase field is solved using the convex splitting method. Several engineering numerical cases are carried out in two‐dimensional computational rectangular domains to verify the applicability and stability of the proposed model, with flow conditions corresponding to relatively low Reynolds numbers. The topological structures of the proposed model adhere to the characteristics of transient two‐phase flows. Moreover, the process of sensitivity analysis is significantly simplified. This study provides a novel approach to transient two‐phase flow topology optimization and offers an optimization design framework for relevant engineering problems.