Sven Groß

Identification of Transport Coefficient Models in Convection-Diffusion Equations

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.

Incremental Identification of Transport Coefficients in Convection-Diffusion Systems

In this paper, an incremental approach for the identification of a model for transport coefficients in convection-diffusion systems on the basis of high-resolution measurement data is presented. The transport is represented by a convection term with known convective velocity and by a diffusion term with an unknown, generally state-dependent transport coefficient. The identification of the transport model for this transport coefficient constitutes an ill-posed nonlinear inverse problem. We present a novel decomposition approach in which this inverse problem is split into a sequence of inverse subproblems. In the first identification step of this incremental approach a source is estimated by solving an affine-linear inverse problem by means of the conjugate gradient method. In the second identification step a nonlinear inverse problem has to be solved to reconstruct a transport coefficient. A Newton-type method using the conjugate gradient method in its inner iteration is used to solve this nonlinear inverse problem of coefficient estimation. Finally, in the third identification step a transport model structure is proposed and identified on the basis of the model-free transport coefficient reconstructed in the two previous steps. The ill-posedness of each inverse problem is examined by using artificially perturbed transient simulation data and appropriate regularization techniques. The identification methodology is illustrated for a three-dimensional convection-diffusion equation which has its origin in the modeling and simulation of energy transport in a laminar wavy film flow.