Downscaling the 2D Bénard convection equations using continuous data assimilation
KAUST DepartmentWater Desalination and Reuse Research Center (WDRC)
Biological and Environmental Sciences and Engineering (BESE) Division
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Environmental Science and Engineering Program
Physical Sciences and Engineering (PSE) Division
Earth Science and Engineering Program
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AbstractWe consider a recently introduced continuous data assimilation (CDA) approach for downscaling a coarse resolution configuration of the 2D Bénard convection equations into a finer grid. In this CDA, a nudging term, estimated as the misfit between some interpolants of the assimilated coarse-grid measurements and the fine-grid model solution, is added to the model equations to constrain the model. The main contribution of this study is a performance analysis of CDA for downscaling measurements of temperature and velocity. These measurements are assimilated either separately or simultaneously, and the results are compared against those resulting from the standard point-to-point nudging approach (NA). Our numerical results suggest that the CDA solution outperforms that of NA, always converging to the true solution when the velocity is assimilated as has been theoretically proven. Assimilation of temperature measurements only may not always recover the true state as demonstrated in the case study. Various runs are conducted to evaluate the sensitivity of CDA to noise in the measurements, the size, and the time frequency of the measured grid, suggesting a more robust behavior of CDA compared to that of NA.
CitationAltaf MU, Titi ES, Gebrael T, Knio OM, Zhao L, et al. (2017) Downscaling the 2D Bénard convection equations using continuous data assimilation. Computational Geosciences. Available: http://dx.doi.org/10.1007/s10596-017-9619-2.
SponsorsThe work of E.S.Titi was supported in part by the ONR grant N00014-15-1-2333 and the NSF grants DMS-1109640 and DMS-1109645.