# Numerical Solutions of Two-Dimensional Mass Transport Equation in Flowing Surface Waters

**Author(s):**Kalinowska M., Rowiński P.

**Volume:**404

**Series:**E-8

The problem of water quality receives an increasing attention of the public, politicians, decision makers nowadays. People have to answer how to achieve any given level and pattern of water quality in particular watercourses and also how to mitigate the catastrophes that are inseparable elements of civilization. The EU water framework directive, which came into force at the end of 2000 (Directive, 2000), changes the way of monitoring, assessing and managing water in European countries. Three groups of quality elements (biological, hydromorphological and physico-chemical) have been identified in the water framework directive as necessary to classify the ecological status of a particular water body.

CONTENTS

1. Introduction, 1

2. Mass transport in open channels, 7

2.1 Introduction, 7

2.2 Physical bases for modeling mass transport in open channels, 8

2.3 Two-dimensional equation of mass transport, 16

2.4 Dispersion coefficients, 18

2.5 Solving 2D transport equation, 20

3. Simplifications of 2D mass transport equation, 23

3.1 Introduction, 23

3.2 Determination of the dispersion tensor coefficients, 24

3.3 Computational tests, 29

4. Numerical methods for 2D transport equation, 45

4.1 Introduction, 45

4.2 Finite difference method, 46

4.3 Discretization of 2D transport equation, 49

4.4 Initial and boundary conditions, 65

5. Properties of considered numerical schemes, 67

5.1 Introduction, 67

5.2 Accuracy - truncation error, 68

5.3 Computation speed and stability, 89

6. Description of RivMix Model, 97

6.1 Introduction, 97

6.2 Simulation parameters, 97

6.3 Algorithm, 99

7. Model verification, 105

7.1 Introduction, 105

7.2 Wide rectangular channel, 105

7.3 Laboratory compound channel, 117

8. Concluding remarks, 129

Appendix A. 2D transport equation, 133

Appendix B. Difference operators used in the book, 135

Appendix C. Dispersion tensor simplifications, 137

Appendix C.1 Instantaneous release of solute, 137

Appendix C.2 Continuous inflow of solute, 148

Appendix D. Boundary conditions, 159

Appendix E. Modified equation, 171

List of symbols, 175

List of acronyms, 179

List of figures, 181

List of tables, 186

References, 189

Index, 198