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

Jürgen Geiser

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

  • Volume: 43, Issue: 6, page 1157-1183
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Geiser, Jürgen. "Discretization methods with analytical characteristic methods for advection-diffusion-reaction equations and 2d applications." ESAIM: Mathematical Modelling and Numerical Analysis 43.6 (2009): 1157-1183. <http://eudml.org/doc/250617>.

@article{Geiser2009,
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. },
author = {Geiser, Jürgen},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Advection-diffusion-reaction equation; embedded analytical solutions; operator-splitting methods; characteristic methods; finite-volume methods; multi-physics; simulation of radioactive waste disposals; advection-diffusion-reaction equation; embedded analytical solutions; characteristic methods; simulation of radioactive waste disposals},
language = {eng},
month = {8},
number = {6},
pages = {1157-1183},
publisher = {EDP Sciences},
title = {Discretization methods with analytical characteristic methods for advection-diffusion-reaction equations and 2d applications},
url = {http://eudml.org/doc/250617},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Geiser, Jürgen
TI - Discretization methods with analytical characteristic methods for advection-diffusion-reaction equations and 2d applications
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2009/8//
PB - EDP Sciences
VL - 43
IS - 6
SP - 1157
EP - 1183
AB - 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.
LA - eng
KW - Advection-diffusion-reaction equation; embedded analytical solutions; operator-splitting methods; characteristic methods; finite-volume methods; multi-physics; simulation of radioactive waste disposals; advection-diffusion-reaction equation; embedded analytical solutions; characteristic methods; simulation of radioactive waste disposals
UR - http://eudml.org/doc/250617
ER -

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