Projection-based reduced order models for flow problems: A variational multiscale approach

Abstract

In this paper we present a Variational Multi-Scale stabilized formulation for a general projection-based Reduced Order Model. In the stabilized formulation we address techniques already analysed in Variational Multi-Scale-Finite Element methods: time-dependent subscales, non-linearity in the subscales approximation and orthogonality between the solution space and the subscale space. Additionally, we describe a mesh based hyper-Reduced Order Model technique and implement a Petrov–Galerkin projection technique. At the end of the article, we test the proposed Reduced Order Model formulation using the incompressible Navier–Stokes problem.