Title: CutFEM topology optimization of 3D laminar incompressible flow problems,
Abstract: This paper studies the characteristics and applicability of the CutFEM
approach as the core of a robust topology optimization framework for 3D laminar
incompressible flow and species transport problems at low Reynolds number (Re <
200). CutFEM is a methodology for discretizing partial differential equations
on complex geometries by immersed boundary techniques. In this study, the
geometry of the fluid domain is described by an explicit level set method,
where the parameters of a level set function are defined as functions of the
optimization variables. The fluid behavior is modeled by the incompressible
Navier-Stokes equations. Species transport is modeled by an advection-diffusion
equation. The governing equations are discretized in space by a generalized
extended finite element method. Face-oriented ghost-penalty terms are added for
stability reasons and to improve the conditioning of the system. The boundary
conditions are enforced weakly via Nit\-sc\-he's method. The emergence of
isolated volumes of fluid surrounded by solid during the optimization process
leads to a singular analysis problem. An auxiliary indicator field is modeled
to identify these volumes and to impose a constraint on the average pressure.
Numerical results for 3D, steady-state and transient problems demonstrate that
the CutFEM analyses are sufficiently accurate, and the optimized designs agree
well with results from prior studies solved in 2D or by density approaches.