Abstract
The transport of fluids and gases in narrow pore systems is described by the transport equation and the material balance equation. In this paper we start with a typical example of such a process and develop the underlying parabolic partial differential equation and the corresponding initial and boundary conditions. Afterwards we describe how to reformulate the problem into a Fredholm integral equation of the first kind, which leads to the boundary element method. Whereas there exists an almost complete approach to the finite difference method and the finite element method, comparably little is known for the BEM. We use the collocation method to solve the Fredholm integral equation of the first kind and present a convergence theorem.
A computer program shows that the the predicted error is in good agreement with the calculated result.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Costabel, M., Boundary integral operators for the heat equation, Integral Equations and Operator Theory 13 (1990), 498–552.
Costabel, M., Onoshi, K., and Wendland, W. L., A Boundary Element Collocation Method for the Neumann Problem of the Heat Equation, in Inverse and Ill-Posed Problems, Academic Press Inc., 1987.
Friedman, A., Partial Differential Equations of Parabolic Type, Prentice-Hall. Inc., 1964.
Herrmann, N., Time discretization of linear parabolic problems, Hung. J. Ind. Chem. 19 (1991), 275–281.
Herrmann, N., Numerical problems in determining pore-size distribution in porous material, Workshop at the University of Budapest, Invited lecture, 1995.
Herrmann, N., Siefer, J., Stephan, E. P., and Wagner, R., Mathematik und Umwelt, Edition Univ. Hannover, Theodor Oppermann Verlag, Hannover, 1994.
Herrmann, N. and Stephan, E. P., FEM und BEM, Einführung, Eigen-druck Inst. f. Angew. Math., Univ. Hannover, 1991.
Iso, Y. Convergence of doundary element solutions for the heat equation, Preprint, 1991.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Herrmann, N. (2000). Mathematical Treatment of Diffusion Processes of Gases and Fluids in Porous Media. In: Chen, Z., Ewing, R.E., Shi, ZC. (eds) Numerical Treatment of Multiphase Flows in Porous Media. Lecture Notes in Physics, vol 552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45467-5_13
Download citation
DOI: https://doi.org/10.1007/3-540-45467-5_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67566-2
Online ISBN: 978-3-540-45467-0
eBook Packages: Springer Book Archive