The Sentinel Method and Its Application to Environmental Pollution Problems

by J.P. Kernevez

Overview

Many environmental problems contain incomplete data in the initial or boundary conditions. How do we solve problems for which some of the initial and/or boundary conditions are unknown? Using a new technique, the sentinel method, this book answers these questions and others as they pertain to inverse problems in environmental pollution, such as pollution of underground and surface waters, thermal pollution, and air pollution.

Product Details

ISBN-13:	9780429607073
Publisher:	CRC Press
Publication date:	07/21/2023
Series:	Mathematical Modeling
Sold by:	Barnes & Noble
Format:	eBook
Pages:	224
File size:	4 MB

About the Author

Jean-Pierre Kernévez

Table of Contents

Introduction

Physical Motivation

Historical Background

Description of the Method

Identification of Pollution in an Aquifer

Modelling of Pollution Transport in an Aquifer

A Sentinel Attached to Each Parameter

Some Examples of Similar Problems

Flow Rate

Numerical Experiments

Sentinels and Pseudo-Inverse

Identification of Pollution in a Lake

Pollution of a Lake

Sentinels

Numerical Experiment

Adjoint State

Numerical Details

HUM Method

Time and Space Discretization

Optimal Emplacement of Sensors

Rectangular Domain

Physical Motivations

Modelling the Physical System

Exact Solution of the Direct Problem

Sentinels for Inversion

Direct Method

Numerical Experiments

Sensitivity to the Size of the Observatory

Sentinels in a River

Oxygen Kinetics and Polluted Water

Convection-Dispersion-Reaction Equation

Exact Solution of the State Equation

Sentinels for a River (Evolution Regime)

Numerical Experiments

Our First Nonlinear Problem

Linear Case

Non-Linear Case

Non-Linear Problems

Position of the Problem

Sentinels of the Linearized Problem

Building the Generalized Inverse

Example

Dispersion Coefficients

Motivation

Linearized System

Linearized System Sentinels

Non-Linear Problem

Numerical Results

Position of a Source

Position of the Problem

Linearization

Sentinels of the Linearized Problem

Non-Linear Problem

Numerical Experiments

Unknown Position and Flow Rate

Sentinels of the Linearized Problem (1)

Sentinels of the Linearized Problem (2)

Moving Source

Recapitulation

Definitions

Inverse Problems

A Convergence Result

Gauss-Newton Method

Shallow Waters

The Movement of Tides: Saint-Venant Shallow Water Equations

Numerical Solution of Shallow Water Equations

Weak Formulation of the Problem

Reaction-Convection-Dispersion Equations

Sentinels

Appendix

Sentinels with a Given Sensibility

Editorial Reviews

Introduces a new technique for solving problems in which some of the initial and/or boundary conditions are unknown, and shows how it can be applied to inverse problems of environmental pollution underground and in surface waters, and thermal and air pollution. The sentinel method is an implementation of the least-squares method particularly well adapted to identifying parameters in distributed ecosystems. Annotation c. by Book News, Inc., Portland, Or.

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