Spatial-dependent and Nonlinear fluid transport: Coupling Framework

Juergen Geiser , Thomas Zacher

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 25 pp.

MSC 2000

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

35K57 Reaction-diffusion equations

Abstract
We introduce a solver method for spatial-dependent and nonlinear fluid transport. 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. The main idea is to apply transformation methods to spatial and nonlinear terms to obtain linear or nonlinear ordinary differential equations. Such differential equations can simpler solved with Laplace-transformation methods or nonlinear solver methods. The nonlinear methods are based on characteristic methods and can be generalised numerically to higher-order TVD methods. In this article we will focus on the derivation of the analytical solutions for spatial- and nonlinear problems, that can be embedded into finite volume methods. At the end of the article we illustrate numerical experiments for different benchmark problems.