A Stabilized Finite Element Framework for Anisotropic Adaptive Topology Optimization of Incompressible Fluid Flows

This paper assesses the feasibility of performing topology optimization of laminar incompressible

flows governed by the steady-state Navier–Stokes equations using anisotropic mesh

adaptation to achieve a high-fidelity description of all fluid–solid interfaces. The present implementation

combines an immersed volume method solving stabilized finite element formulations cast in the

variational multiscale (VMS) framework and level-set representations of the fluid–solid interfaces,

which are used as an a posteriori anisotropic error estimator to minimize interpolation errors under

the constraint of a prescribed number of nodes in the mesh. Numerical results obtained for several

two-dimensional problems of power dissipation minimization show that the optimal designs are

mesh-independent (although the convergence rate does decreases as the number of nodes increases),

agree well with reference results from the literature, and provide superior accuracy over prior studies

solved on isotropic meshes (fixed or adaptively refined).