A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier-Stokes problems

We focus on steady and unsteady Navier-Stokes flow systems in a reduced-order modeling framework based on Proper Orthogonal Decomposition within a levelset geometry description and discretized by an unfitted mesh Finite Element Method. This work extends the approaches of [1 -3] to nonlinear CutFEM discretization. We construct and investigate a unified and geometry independent reduced basis which overcomes many barriers and complications of the past, that may occur whenever geometrical morphings are taking place. By employing a geometry independent reduced basis, we are able to avoid remeshing and transformation to reference configurations, and we are able to handle complex geometries. This combination of a fixed background mesh in a fixed extended background geometry with reduced order techniques appears beneficial and advantageous in many industrial and engineering applications, which could not be resolved efficiently in the past.

Automated summary

This study focuses on steady and unsteady Navier-Stokes flow systems in a reduced-order modeling framework using Proper Orthogonal Decomposition and a levelset geometry description. The discretization is done using an unfitted mesh Finite Element Method and extends the approaches of [1-3] to nonlinear CutFEM discretization. The study constructs and investigates a unified and geometry independent reduced basis that overcomes many barriers and complications that may occur during geometrical morphings.