Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations
arXiv preprint arXiv:2006.07295, 2020•arxiv.org
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 …
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 …
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.
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