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Volume 19, Issue 4
A Computational Study of a Data Assimilation Algorithm for the Two-Dimensional Navier-Stokes Equations

Masakazu Gesho, Eric Olson & Edriss S. Titi

Commun. Comput. Phys., 19 (2016), pp. 1094-1110.

Published online: 2018-04

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We study the numerical performance of a continuous data assimilation (downscaling) algorithm, based on ideas from feedback control theory, in the context of the two-dimensional incompressible Navier-Stokes equations. Our model problem is to recover an unknown reference solution, asymptotically in time, by using continuous-in-time coarse-mesh nodal-point observational measurements of the velocity field of this reference solution (subsampling), as might be measured by an array of weather vane anemometers. Our calculations show that the required nodal observation density is remarkably less than what is suggested by the analytical study; and is in fact comparable to the number of numerically determining Fourier modes, which was reported in an earlier computational study by the authors. Thus, this method is computationally efficient and performs far better than the analytical estimates suggest.

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@Article{CiCP-19-1094, author = {}, title = {A Computational Study of a Data Assimilation Algorithm for the Two-Dimensional Navier-Stokes Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {4}, pages = {1094--1110}, abstract = {

We study the numerical performance of a continuous data assimilation (downscaling) algorithm, based on ideas from feedback control theory, in the context of the two-dimensional incompressible Navier-Stokes equations. Our model problem is to recover an unknown reference solution, asymptotically in time, by using continuous-in-time coarse-mesh nodal-point observational measurements of the velocity field of this reference solution (subsampling), as might be measured by an array of weather vane anemometers. Our calculations show that the required nodal observation density is remarkably less than what is suggested by the analytical study; and is in fact comparable to the number of numerically determining Fourier modes, which was reported in an earlier computational study by the authors. Thus, this method is computationally efficient and performs far better than the analytical estimates suggest.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.060515.161115a}, url = {http://global-sci.org/intro/article_detail/cicp/11121.html} }
TY - JOUR T1 - A Computational Study of a Data Assimilation Algorithm for the Two-Dimensional Navier-Stokes Equations JO - Communications in Computational Physics VL - 4 SP - 1094 EP - 1110 PY - 2018 DA - 2018/04 SN - 19 DO - http://doi.org/10.4208/cicp.060515.161115a UR - https://global-sci.org/intro/article_detail/cicp/11121.html KW - AB -

We study the numerical performance of a continuous data assimilation (downscaling) algorithm, based on ideas from feedback control theory, in the context of the two-dimensional incompressible Navier-Stokes equations. Our model problem is to recover an unknown reference solution, asymptotically in time, by using continuous-in-time coarse-mesh nodal-point observational measurements of the velocity field of this reference solution (subsampling), as might be measured by an array of weather vane anemometers. Our calculations show that the required nodal observation density is remarkably less than what is suggested by the analytical study; and is in fact comparable to the number of numerically determining Fourier modes, which was reported in an earlier computational study by the authors. Thus, this method is computationally efficient and performs far better than the analytical estimates suggest.

Masakazu Gesho, Eric Olson & Edriss S. Titi. (2020). A Computational Study of a Data Assimilation Algorithm for the Two-Dimensional Navier-Stokes Equations. Communications in Computational Physics. 19 (4). 1094-1110. doi:10.4208/cicp.060515.161115a
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