Groundwater contamination : discretization and simulation of systems for convection-diffusion-dispersion reactions / Jurgen Ernst Geiser.

Format:

Book

Author/Creator:

Geiser, Jurgen.

Language:

English

Subjects (All):

Groundwater--Pollution--Simulation methods.

Groundwater.

Hazardous waste sites--Simulation methods.

Hazardous waste sites.

Groundwater--Pollution--Mathematical models.

Dispersion--Mathematical models.

Dispersion.

Discrete-time systems--Mathematical models.

Discrete-time systems.

Discrete geometry.

Physical Description:

1 online resource (172 p.)

Edition:

1st ed.

Place of Publication:

New York : Nova Science Publishers, c2009.

Language Note:

English

Summary:

This work arose from research results of the interdisciplinary centre for scientific computing at the University of Heidelberg as well as of the Humboldt University. The contribution of this work is the simulation of contaminated ground water developed from models about the disposal of severely contaminated material, i.e. radioactive fuels or chemical waste products. The model is based on equations for convection-diffusion-dispersion reactions. The equation in the present book is used for the modelling of a radionuclide transport of pollutants in ground water as well as for chemical irreversible reactions. While solving such problems, so-called multi-scale processes arise. Conventional treatment of black-box discretisation and solution methods are impossible or complicated. Hence, physically motivated methods are used, i.e. to integrate one-dimensional analytical solutions of convection-reaction equations. Especially so-called decomposition methods were emphasized.These methods decouple the different scales and solve the equations based on scales with each other. Therefore the previous coupling errors between the terms of the equations can be controlled and minimised with iterative methods. Furthermore, analytical solutions could be used for comparisons with the numerical solutions. In this work the theoretical derivations of solutions as well as their application in numerical methods for realistic calculations could be acquired. The methods were assembled in a program package that had been developed in a project to evolve a program for modelling the transport of pollutants in ground water. Some realistic damage events could be calculated based on dates from the partner GRS in Braunschweig, Germany.

Contents:

Intro

GROUNDWATER CONTAMINATION: DISCRETIZATION AND SIMULATION OF SYSTEMS FOR CONVECTION-DIFFUSION-DISPERSION REACTIONS

Contents

Preface

Introduction

Modeling

2.1. Introduction and Motivation

2.2. Physics of the Mathematical Model

2.3. Mathematical Model

Discretization

3.1. Introduction

3.2. Finite Volume Method

3.3. Notations for Finite Volume Method

3.4. Discretization of the Convection Equation

3.5. Discretization of the Diffusion-Dispersion Equation

3.6. Discretization of the Reaction Equation

3.7. Discretization of the Convection-Reaction Equation with Embedded Analytical Solutions

Operator-Splitting Methods

4.1. Splitting Method of First Order

4.2. Strang Splitting and Methods of Higher Order

4.3. Iterative Operator-Splitting Method

4.4. Application of the Splitting Methods

4.5. LOD and ADI Methods

4.6. Nonlinear Splitting Methods

4.7. Remarks about the Operator-Splitting Methods

Analytical Solutions for One-Dimensional Convection-Reaction Equations

5.1. Analytical Solutions for Convection-Reaction Equations with Variable Retardation Factors

5.2. Calculating the Analytical Solution of Mass

Iterative Methods and Multigrid Methods

6.1. Introduction

6.2. Linear Algebra

6.3. Linear Iterative Method

6.4. Introduction to Multigrid Methods

Software Package r3t

7.1. Introduction

7.2. Rough Structuring of the Software Packages

7.3. UG Software Toolbox

7.4. Software Package d3f

7.5. Software Package r3t

Model Problems

8.1. Introduction for Model Problems

8.2. Error Norms and Orders of Convergence to Evaluate Nu-merical Results

8.3. One-Dimensional Model Problems for Linear Equilibrium-Sorption.

8.4. Two-Dimensional Model Problem for Linear Equilibrium-Sorption

8.5. Realistic Model for a Potential Damage Event

Outlook

9.1. Conclusion and Outlook

Appendix A Properties, Transformable Functions, and Partial Fraction Expansion of the Laplace Transformation

Appendix B General Solutions for Ordinary Differential Equations

References

Index.

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [149]-158) and index.

ISBN:

1-60876-524-5

OCLC:

847650583