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.
Table of Contents
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.