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Volume 40, Issue 1
Removing Splitting/Modeling Error in Projection/Penalty Methods for Navier-Stokes Simulations with Continuous Data Assimilation

Elizabeth Hawkins, Leo G. Rebholz & Duygu Vargun

DOI: 10.4208/cmr.2023-0008

Commun. Math. Res., 40 (2024), pp. 1-29.

Published online: 2023-12

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  • Abstract

We study continuous data assimilation (CDA) applied to projection and penalty methods for the Navier-Stokes (NS) equations. Penalty and projection methods are more efficient than consistent NS discretizations, however are less accurate due to modeling error (penalty) and splitting error (projection). We show analytically and numerically that with measurement data and properly chosen parameters, CDA can effectively remove these splitting and modeling errors and provide long time optimally accurate solutions.

  • Keywords

Navier-Stokes equations, projection method, penalty method, continuous data assimilation.

  • AMS Subject Headings

65M12, 65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-40-1, author = {Hawkins , ElizabethRebholz , Leo G. and Vargun , Duygu}, title = {Removing Splitting/Modeling Error in Projection/Penalty Methods for Navier-Stokes Simulations with Continuous Data Assimilation}, journal = {Communications in Mathematical Research }, year = {2023}, volume = {40}, number = {1}, pages = {1--29}, abstract = {

We study continuous data assimilation (CDA) applied to projection and penalty methods for the Navier-Stokes (NS) equations. Penalty and projection methods are more efficient than consistent NS discretizations, however are less accurate due to modeling error (penalty) and splitting error (projection). We show analytically and numerically that with measurement data and properly chosen parameters, CDA can effectively remove these splitting and modeling errors and provide long time optimally accurate solutions.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2023-0008}, url = {http://global-sci.org/intro/article_detail/cmr/22279.html} }
TY - JOUR T1 - Removing Splitting/Modeling Error in Projection/Penalty Methods for Navier-Stokes Simulations with Continuous Data Assimilation AU - Hawkins , Elizabeth AU - Rebholz , Leo G. AU - Vargun , Duygu JO - Communications in Mathematical Research VL - 1 SP - 1 EP - 29 PY - 2023 DA - 2023/12 SN - 40 DO - http://doi.org/10.4208/cmr.2023-0008 UR - https://global-sci.org/intro/article_detail/cmr/22279.html KW - Navier-Stokes equations, projection method, penalty method, continuous data assimilation. AB -

We study continuous data assimilation (CDA) applied to projection and penalty methods for the Navier-Stokes (NS) equations. Penalty and projection methods are more efficient than consistent NS discretizations, however are less accurate due to modeling error (penalty) and splitting error (projection). We show analytically and numerically that with measurement data and properly chosen parameters, CDA can effectively remove these splitting and modeling errors and provide long time optimally accurate solutions.

Elizabeth Hawkins, Leo G. Rebholz & Duygu Vargun. (2023). Removing Splitting/Modeling Error in Projection/Penalty Methods for Navier-Stokes Simulations with Continuous Data Assimilation. Communications in Mathematical Research . 40 (1). 1-29. doi:10.4208/cmr.2023-0008
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