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

TL;DR

This paper introduces a reduced order modeling approach for steady and unsteady Navier-Stokes equations that uses a geometry-independent basis and unfitted mesh finite element discretization, enabling efficient handling of complex geometries without remeshing.

Contribution

It develops a unified reduced basis method based on Proper Orthogonal Decomposition that overcomes previous limitations related to geometrical morphings and complex domain handling.

Findings

Avoids remeshing and transformation to reference configurations

Handles complex geometries efficiently

Applicable to industrial and engineering problems

Abstract

This work focuses on steady and unsteady Navier-Stokes equations in a reduced order modeling framework. The methodology proposed is based on a Proper Orthogonal Decomposition within a levelset geometry description and the problems of interest are discretized with an unfitted mesh Finite Element Method. 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.