1st Edition

Adaptive Method of Lines

Edited By A, Vande Wouwer, Ph. Saucez, W.E. Schiesser Copyright 2001
    432 Pages 50 B/W Illustrations
    by Chapman & Hall

    The general Method of Lines (MOL) procedure provides a flexible format for the solution of all the major classes of partial differential equations (PDEs) and is particularly well suited to evolutionary, nonlinear wave PDEs. Despite its utility, however, there are relatively few texts that explore it at a more advanced level and reflect the method's current state of development.

    Written by distinguished researchers in the field, Adaptive Method of Lines reflects the diversity of techniques and applications related to the MOL. Most of its chapters focus on a particular application but also provide a discussion of underlying philosophy and technique. Particular attention is paid to the concept of both temporal and spatial adaptivity in solving time-dependent PDEs. Many important ideas and methods are introduced, including moving grids and grid refinement, static and dynamic gridding, the equidistribution principle and the concept of a monitor function, the minimization of a functional, and the moving finite element method. Applications addressed include shallow water flow, combustion and flame propagation, transport in porous media, gas dynamics, chemical engineering processes, solitary waves, and magnetohydrodynamics.

    As the first advanced text to represent the modern era of the method of lines, this monograph offers an outstanding opportunity to discover new concepts, learn new techniques, and explore a wide range of applications.

    Introduction
    Application of the Adaptive Method of Lines to Nonlinear Wave Propagation Problems
    Adaptive MOL for Magneto-Hydrodynamic PDE Models
    Development of a 1-D Error-Minimizing Moving Adaptive Grid Method
    An Adaptive Method of Lines Approach for Modelling Flow and Transport in Rivers
    An Adaptive Mesh Algorithm for Free Surface Flows in General Geometries, M. Sussman
    The Solution of Steady PDEs on Adjustable Meshes in Multidimensions Using Local Descent Methods
    Adaptive Linearly Implicit Methods for Heat and Mass Transfer Problems
    Linearly Implicit Adaptive Schemes for Singular Reaction-Diffusion Equations
    Unstructured Mesh MOL Solvers for Reacting Flow Problems
    Two-Dimensional Model of a Reaction Bonded Aluminum Oxide Cylinder
    Method of Lines within the Simulation Environment DIVA for Chemical Processes.

    Biography

    A Vande Wouwer, Ph. Saucez, W.E. Schiesser