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

References in corpus (1)

• A monolithic and a partitioned Reduced Basis Method for Fluid-Structure Interaction problems

Cited by in corpus (3)

• Geometrically Parametrised Reduced Order Models for the Study of Hysteresis of the Coanda Effect in Finite Element-based Incompressible Fluid Dynamics
• Discrete Empirical Interpolation and unfitted mesh FEMs: application in PDE-constrained optimization
• Reduced Basis, Embedded Methods and Parametrized Levelset Geometry