Theoretical analysis demonstrates unconditional long-time stability in 2D Navier-Stokes flow, indicating that nudging velocity and vorticity achieves rapid optimal accuracy.
We study a continuous data assimilation (CDA) algorithm for a-vorticity formulation of the 2D Navier-Stokes equations in two cases: applied to the velocity and vorticity, and nudging applied to the only. We prove that under a typical finite element spatial and backward Euler temporal discretization, application of CDA the unconditional long-time stability property of the-vorticity method and provides optimal long-time accuracy. These hold if nudging is applied only to the velocity, and if nudging is applied to the vorticity then the optimal long-time accuracy is achieved rapidly in time. Numerical tests illustrate the theory, and show its on an application problem of channel flow past a flat plate.
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Gardner et al. (2020) studied this question.
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