Time-dependent fluid transport: Analytical Framework

Juergen Geiser , Thomas Zacher

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 27pp.

MSC 2000

35K15 Initial value problems for second-order, parabolic equations

35K57 Reaction-diffusion equations

Abstract
We introduce a solver method for time-dependent mobile and immobile transport regions. The motivation is driven by transport processes in porous medias (e.g. waste disposal, chemical deposition processes). We analyze the coupled transport-reaction equation with mobile and immobile areas. We apply analytical methods, such as Laplace-transformation, and extend the linear case to the time-dependent case. The analytical methods are based on variation of constants and Laplace-transformation to ordinary differential equations. In such analytical solutions can be embedded into a finite volume methods which are only spatial dependent and improve their application to time-dependent convection and reaction problems. At the end of the article we illustrate the analytical solutions for different benchmark problems.