On the virtual element method for topology optimization of non-Newtonian fluid-flow problems

This paper presents some virtual element method (VEM) applications for topology optimization of non-Newtonian fluidflow problems in arbitrary two-dimensional domains. The objective is to design an optimal layout for the incompressible non-Newtonian fluid flow, governed by the Navier-Stokes-Brinkman equations, to minimize the viscous drag. The porosity approach is used in the topology optimization formulation. The VEM is used to solve the governing boundary value problem. The key feature distinguishing the VEM from the classical finite element method is that the local basis functions in the VEM are only implicitly known. Instead, the VEM uses local projection operators to describe each element's rigid body motion and constant strain components. Therefore, the VEM can handle meshes with arbitrarily shaped elements. Several numerical examples are provided to demonstrate the efficacy and efficiency of the VEM for the topology optimization of fluid-flow problems. A MATLAB code for reproducing the results provided in this paper is freely available at https://github.com/mampueros/VEM_TopOpt_FluidFlow.