Identification of Transport Coefficient Models in Convection-Diffusion Equations

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. 3249-3269], 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.