9,659 research outputs found
Assimilation of nearly turbulent Rayleigh-B\'enard flow through vorticity or local circulation measurements: a computational study
We introduce a continuous (downscaling) data assimilation algorithm for the
2D B\'enard convection problem using vorticity or local circulation
measurements only. In this algorithm, a nudging term is added to the vorticity
equation to constrain the model. Our numerical results indicate that the
approximate solution of the algorithm is converging to the unknown reference
solution (vorticity and temperature) corresponding to the measurements of the
2D B\'enard convection problem when only spatial coarse-grain measurements of
vorticity are assimilated. Moreover, this convergence is realized using data
which is much more coarse than the resolution needed to satisfy rigorous
analytical estimates
Data Assimilation algorithm for 3D B\'enard convection in porous media employing only temperature measurements
In this paper we propose a continuous data assimilation (downscaling)
algorithm for the B\'enard convection in porous media using only coarse mesh
measurements of the temperature. In this algorithm, we incorporate the
observables as a feedback (nudging) term in the evolution equation of the
temperature. We show that under an appropriate choice of the nudging parameter
and the size of the mesh, and under the assumption that the observed data is
error free, the solution of the proposed algorithm converges at an exponential
rate, asymptotically in time, to the unique exact unknown reference solution of
the original system, associated with the observed (finite dimensional
projection of) temperature data. Moreover, we note that in the case where the
observational measurements are not error free, one can estimate the error
between the solution of the algorithm and the exact reference solution of the
system in terms of the error in the measurements.Comment: arXiv admin note: text overlap with arXiv:1504.0597
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