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Discretization methods with analytical characteristicmethods for advection-diffusion-reaction equations and 2d applications

Published online by Cambridge University Press:  01 August 2009

Jürgen Geiser
Jürgen Geiser*
Affiliation:
Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany. geiser@mathematik.hu-berlin.de
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Abstract

Our studies are motivated by a desire to model long-time simulations of possible scenarios for a waste disposal. Numerical methods are developed for solving the arising systems of convection-diffusion-dispersion-reaction equations, and the received results of several discretization methods are presented. We concentrate on linear reaction systems, which can be solved analytically. In the numerical methods, we use large time-steps to achieve long simulation times of about 10 000 years. We propose higher-order discretization methods, which allow us to use large time-steps without losing accuracy. By decoupling of a multi-physical and multi-dimensional equation, simpler physical and one-dimensional equations are obtained and can be discretized with higher-order methods. The results can then be coupled with an operator-splitting method. We discuss benchmark problems given in the literature and real-life applications. We simulate a radioactive waste disposals with underlying flowing groundwater. The transport and reaction simulations for the decay chains are presented in 2d realistic domains, and we discuss the received results. Finally, we present our conclusions and ideas for further works.

Keywords

Advection-diffusion-reaction equationembedded analytical solutionsoperator-splitting methodscharacteristic methodsfinite-volume methodsmulti-physicssimulation of radioactive waste disposals
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 6 , November 2009 , pp. 1157 - 1183
Copyright
© EDP Sciences, SMAI, 2009

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