Energy based discretization of a class of distributed parameters processes comparison with classical approach

This paper deals with model reduction of infinite dimensional systems described by PDEs. It focuses on one dimensional systems as tubular reactors and adsorption processes derived from mass transport phenomena. The proposed method is based on energetic considerations. First, concepts of network modeling are used to stress the structure of the power transmission within the spatial domain and through the boundary. It is shown how to define the port variables such that the interconnection between dissipation and accumulation elements is power preserving. Based on this definition, the discretization method aims at preserving the structure associated with mass and power balances during the reduction. Finally the proposed methodology is compared with a finite difference method on an adsorption process. It is shown that in the centered approximation case, the proposed method avoids oscillations obtained from finite difference method.