TY - RPRT
A1 - Printsypar, G.
A1 - Ciegis, R.
T1 - On convergence of a discrete problem describing transport processes in the pressing section of a paper machine including dynamic capillary effects: one-dimensional case
N2 - 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.
T3 - Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) - 210
Y1 - 2011
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2986
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-29867
ER -