Paper Info
Title
On convergence of a discrete problem describing transport processes in the pressing section of a paper machine including dynamic capillary effects: One-dimensional case
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.
Year
DOI
Venue
2012
10.1016/j.cam.2012.03.017
J. Computational Applied Mathematics
Keywords
Field
DocType
one-dimensional case,proposed finite difference scheme,continuous problem,discrete solution converges,pressing section,main theorem,flow regime,filtration process,dynamic capillary effect,finite volume method,paper machine,discrete problem,dynamic capillary pressure model,different mesh size,discrete solution
Convergence (routing),Mathematical optimization,System of linear equations,Mathematical analysis,Capillary pressure,Compact space,Paper machine,Rate of convergence,Finite volume method,Conservation of mass,Mathematics
Journal
Volume
Issue
ISSN
236
14
0377-0427
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
G. Printsypar121.29
R. iegis200.34