NDLI: Identification of Transport Coefficient Models in Convection-Diffusion Equations

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Gro, Sven Marquardt, Wolfgang Reusken, Arnold Mhamdi, Adel Karalashvili, Maka
Copyright Year	2011
Abstract	A rigorous method is presented for the systematic identification of the structure and the parameters of transport coefficient models in three-dimensional, transient convection-diffusion systems using high-resolution measurement data. The transport is represented by a convection term with known convective velocity and a diffusion term with an unknown, generally state-dependent, transport coefficient. The identification of a transport coefficient model constitutes an ill-posed, highly nonlinear inverse problem. In our previous work [Karalashvili et al., SIAM J. Sci. Comput., 30 (2008), pp. 32493269], we presented a novel incremental identification method, which decomposes this inverse problem into easier-to-handle inverse subproblems. This way, the incremental identification method not only allows for the identification of the structure and the parameters of the model, but also supports the rigorous decision making on the best-suited transport model structure. Due to the decomposition approach, the identified transport model structure and parameters are subject to errors. To cope with the error propagation inherent in the incremental method, the present work suggests a model correction procedure as a supplement to the incremental identification method of our previous work, which results in a transport model of higher precision. The correction refers to both the model structure and parameters. No a priori knowledge on the unknown transport model structure is necessary. The identification approach is numerically illustrated for a three-dimensional, transient convection-diffusion equation which has its origin in the modeling and simulation of energy transport in a laminar wavy film flow.
Starting Page	303
Ending Page	327
Page Count	25
File Format	PDF
ISSN	10648275
DOI	10.1137/09077360X
e-ISSN	10957197
Issue Number	1
Volume Number	33
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2011-02-22
Access Restriction	Subscribed
Subject Keyword	convection-diffusion equation inverse problem modeling identification regularization inexact Newton-type method Factorization of matrices Determinants, permanents, other special matrix functions model selection parameter estimation transport Matrix inversion, generalized inverses
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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