Variational Multiscale Proper Orthogonal Decomposition: Navier-Stokes Equations
Abstract
We develop a variational multiscale proper orthogonal decomposition reduced-order model for turbulent incompressible Navier-Stokes equations. The error analysis of the full discretization of the model is presented. All error contributions are considered: the spatial discretization error (due to the finite element discretization), the temporal discretization error (due to the backward Euler method), and the proper orthogonal decomposition truncation error. Numerical tests for a three-dimensional turbulent flow past a cylinder at Reynolds number Re=1000 show the improved physical accuracy of the new model over the standard Galerkin and mixing-length proper orthogonal decomposition reduced-order models. The high computational efficiency of the new model is also showcased. Finally, the theoretical error estimates are confirmed by numerical simulations of a two-dimensional Navier-Stokes problem.
Cite
@article{arxiv.1210.7389,
title = {Variational Multiscale Proper Orthogonal Decomposition: Navier-Stokes Equations},
author = {Traian Iliescu and Zhu Wang},
journal= {arXiv preprint arXiv:1210.7389},
year = {2013}
}
Comments
30 pages, 5 figures