A Proper-Orthogonal Decomposition Variational Multiscale Approximation Method for a Generalized Oseen Problem

Abstract EN

We introduce the variational multiscale (VMS) stabilization for the reduced-order modeling of incompressible flows.

It is well known that the proper orthogonal decomposition (POD) technique in reduced-order modeling experiences numerical instability when applied to complex flow problems.

In this case a POD discretization naturally separates out structures which corresponding to the energy cascade on large and small scales, in order, a VMS approach is natural.

In this paper, we provide the mathematical background necessary for implementing VMS to a POD-Galerkin model of a generalized Oseen problem.

We provide theoretical evidence which indicates the consistency of utilizing a VMS approach in the stabilization of reduced order flows.

In addition we provide numerical experiments indicating that VMS improves fidelity in reproducing the qualitative properties of the flow.