Variational multiscale proper orthogonal decomposition: Navier-stokes equations

Mixed Finite Element Formulation and Error Estimates Based on Proper Orthogonal Decomposition for the Nonstationary Navier-Stokes Equations

In this paper, proper orthogonal decomposition (POD) is used for model reduction of mixed finite element (MFE) for the nonstationary Navier–Stokes equations and error estimates between a reference solution and the POD solution of reduced MFE formulation are derived. The basic idea of this reduction technique is that ensembles of data are first compiled from transient solutions computed equation...

Finite element error analysis of a variational multiscale method for the Navier-Stokes equations

A Finite Element Variational Multiscale Method for the Navier-Stokes Equations

This paper presents a variational multiscale method (VMS) for the incompressible Navier–Stokes equations which is defined by a large scale space LH for the velocity deformation tensor and a turbulent viscosity νT . The connection of this method to the standard formulation of a VMS is explained. The conditions on LH under which the VMS can be implemented easily and efficiently into an existing f...

A Variational Multiscale Newton–schur Approach for the Incompressible Navier–stokes Equations

Abstract. In the following paper, we present a consistent Newton-Schur solution approach for variational multiscale formulations of the time-dependent Navier–Stokes equations in three dimensions. The main contributions of this work are a systematic study of the variational multiscale method for three-dimensional problems, and an implementation of a consistent formulation suitable for large prob...

Model Reduction Based on Proper Generalized Decomposition for the Stochastic Steady Incompressible Navier-Stokes Equations

In this paper we consider a Proper Generalized Decomposition method to solve the steady incompressible Navier–Stokes equations with random Reynolds number and forcing term. The aim of such technique is to compute a low-cost reduced basis approximation of the full Stochastic Galerkin ∗O.P. Le Mâıtre and A. Nouy are partially supported by GNR MoMaS (ANDRA, BRGM, CEA, EdF, IRSN, PACEN-CNRS) and by...