2015/04/22 by Aseel Farhat, Evelyn Lunasin, Edriss S. Titi · 95 citations
Earth and Planetary Sciences · Engineering · Mathematics · #Assimilation (phonology) #Component (thermodynamics) #Computational Fluid Dynamics and Aerodynamics #Data assimilation #Field (mathematics) #Fluid Dynamics and Turbulent Flows #Mathematics #Mechanics #Meteorological Phenomena and Simulations #Meteorology #Philosophy #Physics #Pure mathematics #Thermodynamics #Vector field #math.AP
paper · pdf · doi:10.1007/s00021-015-0225-6
published in Journal of Mathematical Fluid Mechanics 18(1), 1-23 (Birkhäuser)
arxiv created 2015/04/22 · openalex publication_date 2015/10/30 · arxiv updated 2016/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce a continuous data assimilation (downscaling) algorithm for the two-dimensional Navier-Stokes equations employing coarse mesh measurements of only one component of the velocity field. This algorithm can be implemented with a variety of finitely many observables: low Fourier modes, nodal values, finite volume averages, or finite elements. We provide conditions on the spatial resolution of the observed data, under the assumption that the observed data is free of noise, which are sufficient to show that the solution of the algorithm approaches, at an exponential rate asymptotically in time, to the unique exact unknown reference solution, of the 2D Navier-Stokes equations, associated with the observed (finite dimensional projection of) velocity.