Continuous data assimilation for the 2D Bénard convection through velocity measurements alone
By A. Farhat, M. Jolly, Edriss S. Titi. 2014
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© 2015 Elsevier B.V. An algorithm for continuous data assimilation for the two-dimensional Benard convection problem is introduced and analyzed. It is inspired by the data assimilation algorithm developed for the Navier-Stokes equations, which allows for the implementation of variety of observables: low Fourier modes, nodal values, finite volume averages, and finite elements. The novelty here is that the observed data is obtained for the velocity field alone; i.e. no temperature measurements are needed for this algorithm. 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, the unique exact unknown solution of the Benard convection problem associated with the observed (finite dimensional projection of) velocity.
Subfields: Atmospheric Science, Computational Mechanics
View Paper: https://www.semanticscholar.org/paper/9740f4ec8388feed66ad62412cb746c4f5ee3dfe
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In Computational Mechanics
Citations in the corpus
- Global in time stability and accuracy of IMEX-FEM data assimilation schemes for Navier–Stokes equations (2018, background): “2]. In [32], several nonlinear versions of this approach were proposed and studied. In addition to the results discussed here, a large amount of recent literature has built upon this idea; see, e.g., [1, 6, 14, 15, 16, 17, 18, 20, 23, 29, 30, 36]. Although extensive research has been done on the the”