Mobile and immobile gaseous transport: Embedded analytical solutions to finite volume methods

Juergen Geiser , Thomas Zacher

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 40 pp.

MSC 2000

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

35K57 Reaction-diffusion equations

Abstract
We introduce a solver method for mobile and immobile transport regions. The motivation is driven by deposition processes based on chemical vapor problems. We analyze the coupled transport-reaction equation with mobile and immobile areas. We apply analytical methods, such as Laplace-transformation, and for the numerical methods we apply Godunov's scheme, see [Godunov59] and [Leveque02]. The method is based numerically on flux-based characteristic methods and is an attractive alternative to the classical higher-order TVD methods, see \cite{hart83}. In this article we will focus on the derivation of the analytical solutions for general and special solutions of the characteristic methods, that are embedded into a finite volume method. At the end of the article we illustrate the higher-order method for different benchmark problems. Finally the method is proposed with realistic results.