1st Edition

The Sentinel Method and Its Application to Environmental Pollution Problems

By J.P. Kernevez Copyright 1997

    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.

    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
    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
    Dispersion Coefficients
    Linearized System
    Linearized System Sentinels
    Non-Linear Problem
    Numerical Results
    Position of a Source
    Position of the Problem
    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
    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 with a Given Sensibility and Duality
    Existence of a Solution and Functional Spaces


    Jean-Pierre Kernévez