Continuous data assimilation for the three-dimensional Brinkman-Forchheimer-extended Darcy model

被引:105
作者
Markowich, Peter A. [1 ]
Titi, Edriss S. [2 ]
Trabelsi, Saber [1 ]
机构
[1] King Abdullah Univ Sci & Technol, Div Math & Comp Sci & Engn, Thuwal 239556900, Saudi Arabia
[2] Texas A&M Univ, Dept Math, 3368 TAMU, College Stn, TX 77843 USA
基金
美国国家科学基金会;
关键词
Brinkman-Forchheimer-extended Darcy model; data assimilation; down-scaling; HEAT-TRANSFER; ATTRACTORS; EXISTENCE; FLOW; EQUATIONS;
D O I
10.1088/0951-7715/29/4/1292
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:1292 / 1328
页数:37
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