Continuous data assimilation for the three-dimensional Brinkman–Forchheimer-extended Darcy model
By Peter A. Markowich, Edriss S. Titi, S. Trabelsi. 2015
173 citations recorded by the source corpus.
In 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.
Subfields: Atmospheric Science, Computational Mechanics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/7524168ee7a3950697aec72e34e38672b053f9ad
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In Computational Mechanics
In Computational Theory and Mathematics
Citations in the corpus
- Energy equality for the 3D critical convective Brinkman–Forchheimer equations (2016, background): “when the Darcy law for a porous medium no longer applies (for more details see [13], [12] and the discussion in [11]).”