Incremental Identification of Transport Coefficients in Convection-Diffusion Systems

Maka Karalashvili, Sven Groß, Adel Mhamdi, Arnold Reusken, Wolfgang Marquardt
2008 SIAM Journal on Scientific Computing  
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
more » ... t 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. ; published electronically DATE. This work was supported by Deutsche Forschungsgemeinschaft (DFG) within the Collaborative Research Center (SFB) 540 "Model-based experimental analysis of kinetic phenomena in fluid multiphase reactive systems."
doi:10.1137/070692388 fatcat:llrsmselj5h7rhy2pgj6ianbyi