Michael Jolly, Indiana University

Assimilation of Rayleigh-Benard convection using only velocity data

A. Farhat, H. Johnston, E. Titi


An algorithm for continuous data assimilation of the two-dimensional Rayleigh-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 a variety of observables: low Fourier modes, nodal values, finite volume averages, and finite elements. The novelty here is that the observed data is of 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 convection problem associated with the observed (finite dimensional projection of) velocity. Computations are presented to demonstrate that the algorithm is effective using much coarser data than required for the rigorous analysis.

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