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On convergence of a discrete problem describing transport processes in the pressing section of a paper machine including dynamic capillary effects: one-dimensional case

  • 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 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 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 continuous problem. At the end we present numerical studies for the rate of convergence.

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Author:G. Printsypar, R. Ciegis
URN (permanent link):urn:nbn:de:hbz:386-kluedo-29867
Serie (Series number):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (210)
Document Type:Report
Language of publication:English
Publication Date:2012/04/18
Year of Publication:2011
Publishing Institute:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Date of the Publication (Server):2012/04/18
Number of page:37
Faculties / Organisational entities:Fraunhofer (ITWM)
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 15.02.2012