Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations
Abstract
We study a continuous data assimilation (CDA) algorithm for a velocity-vorticity formulation of the 2D Navier-Stokes equations in two cases: nudging applied to the velocity and vorticity, and nudging applied to the velocity only. We prove that under a typical finite element spatial discretization and backward Euler temporal discretization, application of CDA preserves the unconditional long-time stability property of the velocity-vorticity method and provides optimal long-time accuracy. These properties hold if nudging is applied only to the velocity, and if nudging is also applied to the vorticity then the optimal long-time accuracy is achieved more rapidly in time. Numerical tests illustrate the theory, and show its effectiveness on an application problem of channel flow past a flat plate.
Keywords
Cite
@article{arxiv.2006.07295,
title = {Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations},
author = {Matthew Gardner and Adam Larios and Leo G. Rebholz and Duygu Vargun and Camille Zerfas},
journal= {arXiv preprint arXiv:2006.07295},
year = {2020}
}
Comments
28 pages, 8 figures, 2 tables