Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. On convergence of a discrete problem describing transport processes in the pressing section of a paper machine including dynamic capillary effects: Onedimensional case
 Journal of computational and applied mathematics 236 (2012), No.14, pp.34093425 ISSN: 03770427 ISSN: 0771050X 

 English 
 Journal Article 
 Fraunhofer ITWM () 
Abstract
This work presents a proof of convergence of a discrete solution to a continuous one. At first, the continuous problem is stated as a system of equations which describe the filtration process in the pressing section of a paper machine. Two flow regimes appear in the modeling of this problem. The model for the saturated flow is presented by the Darcy's law and the mass conservation. The second regime is described by the Richards' approach together with a dynamic capillary pressure model. The finite volume method is used to approximate the system of PDEs. Then, the existence of a discrete solution to the proposed finite difference scheme is proven. Compactness of the set of all discrete solutions for different mesh sizes is proven. The main theorem shows that the discrete solution converges to the solution of the continuous problem. At the end we present numerical studies for the rate of convergence.