Topology Optimization for Unsteady Non‐Newtonian Fluid Flows Using the Streamline Upwind Petrov‐Galerkin With Penalty Finite Element Method

ABSTRACT This paper addresses the topology optimization of unsteady incompressible non‐Newtonian fluid flows. To reduce computational cost and improve efficiency, fluid simulations are performed using a penalty finite element method (PFEM) that decouples the velocity and pressure computations. Numerical oscillations induced by flow inertia are suppressed by streamline upwind Petrov–Galerkin (SUPG) stabilization. The optimization problem is formulated in a density‐based framework and is solved with gradient‐based algorithms, with the instantaneous minimum energy dissipation adopted as the objective. Several representative two‐ and three‐dimensional cases are presented, followed by a comprehensive analysis to evaluate the effects of unsteady dynamics and non‐Newtonian characteristics on both the optimized process and results. The findings broaden the applicability of fluid flow topology optimization and provide new insights for designing under unsteady, non‐Newtonian conditions.