Continuous data assimilation for the three-dimensional Brinkman–Forchheimer-extended Darcy model
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Division of Math and Computer Sci. and Eng., King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
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AbstractIn this paper we introduce and analyze an algorithm for continuous data assimilation for a three-dimensional Brinkman-Forchheimer-extended Darcy (3D BFeD) model of porous media. This model is believed to be accurate when the flow velocity is too large for Darcy's law to be valid, and additionally the porosity is not too small. The algorithm is inspired by ideas developed for designing finite-parameters feedback control for dissipative systems. It aims to obtain improved estimates of the state of the physical system by incorporating deterministic or noisy measurements and observations. Specifically, the algorithm involves a feedback control that nudges the large scales of the approximate solution toward those of the reference solution associated with the spatial measurements. In the first part of the paper, we present a few results of existence and uniqueness of weak and strong solutions of the 3D BFeD system. The second part is devoted to the convergence analysis of the data assimilation algorithm. © 2016 IOP Publishing Ltd & London Mathematical Society.
CitationMarkowich PA, Titi ES, Trabelsi S (2016) Continuous data assimilation for the three-dimensional Brinkman–Forchheimer-extended Darcy model. Nonlinearity 29: 1292–1328. Available: http://dx.doi.org/10.1088/0951-7715/29/4/1292.
SponsorsEST is thankful to the kind hospitality of KAUST where this work was started. EST also acknowledges the partial support of the National Science Foundation through grants number DMS-1109640 and DMS-1109645. The research of P A Markowich and S Trabelsi reported in this publication was supported by the King Abdullah University of Science and Technology.