Combining existing numerical models with data assimilation using weighted least-squares finite element methods.

Autor: Rajaraman PK; Chemical and Biological Engineering Department, Montana State University, Bozeman, MT, 59717, USA., Manteuffel TA; Department of Applied Mathematics, University of Colorado, Boulder, CO, 80309, USA., Belohlavek M; Mayo Clinic Arizona, Scottsdale, AZ, 85259, USA., Heys JJ; Chemical and Biological Engineering Department, Montana State University, Bozeman, MT, 59717, USA.
Jazyk: angličtina
Zdroj: International journal for numerical methods in biomedical engineering [Int J Numer Method Biomed Eng] 2017 Jan; Vol. 33 (1). Date of Electronic Publication: 2016 Apr 20.
DOI: 10.1002/cnm.2783
Abstrakt: A new approach has been developed for combining and enhancing the results from an existing computational fluid dynamics model with experimental data using the weighted least-squares finite element method (WLSFEM). Development of the approach was motivated by the existence of both limited experimental blood velocity in the left ventricle and inexact numerical models of the same flow. Limitations of the experimental data include measurement noise and having data only along a two-dimensional plane. Most numerical modeling approaches do not provide the flexibility to assimilate noisy experimental data. We previously developed an approach that could assimilate experimental data into the process of numerically solving the Navier-Stokes equations, but the approach was limited because it required the use of specific finite element methods for solving all model equations and did not support alternative numerical approximation methods. The new approach presented here allows virtually any numerical method to be used for approximately solving the Navier-Stokes equations, and then the WLSFEM is used to combine the experimental data with the numerical solution of the model equations in a final step. The approach dynamically adjusts the influence of the experimental data on the numerical solution so that more accurate data are more closely matched by the final solution and less accurate data are not closely matched. The new approach is demonstrated on different test problems and provides significantly reduced computational costs compared with many previous methods for data assimilation. Copyright © 2016 John Wiley & Sons, Ltd.
(Copyright © 2016 John Wiley & Sons, Ltd.)
Databáze: MEDLINE
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