Incremental Identification of Transport Phenomena in Convection-diffusion Systems

In this paper an incremental approach for the identification of transport phenomena 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 reconstruction of 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. The inverse problems arising in the different identification steps of this incremental approach are solved by means of the conjugate gradient method in which an adjoint problem is solved for gradient computation. 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 that has its origin in the modeling and simulation of energy transport in a laminar wavy film flow.