Transport and Chemical Reaction: Characteristics Method and Splitting Methods

Juergen Geiser , Asgar Jamneshan

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 37 pp.

MSC 2000

35K25 General theory of higher-order, parabolic equations

35K20 Boundary value problems for second-order, parabolic equations

Abstract
In this paper we present computational schemes for solving transport and chemical reaction processes. The model is based on a convection-diffusion-reaction equation which models our fluid dynamics of the deposition process. For the spatial discretization we combine characteristics methods for the advection equations and use finite volume methods for the diffusion equation. The reaction parts are solved analytically and the solutions are embedded into the spatial discretized advection parts. We present decomposition methods in time to couple the different scales of the multi-component transport equations. The different time-scales are coupled by transfer-operators and we discuss a multi-scale solver. In the numerical experiments we present a microscopic model for pratical transport. The accuracy of the methods are discussed.