Effective Computational Methods for Wave Propagation

Series:
Numerical Insights
Published:
February 25, 2008 by Chapman and Hall/CRC - 712 Pages
Editor(s):
Nikolaos A. Kampanis, Hellas Institute, Iraklion, Greece; Vassilios Dougalis, FORTH/IACM, Heraklion, Crete, Greece; John A. Ekaterinaris, FORTH/IACM, Heraklion, Crete, Greece

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$145.95
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ISBN 9781584885689
Cat# C5688
 

Features

  • Presents contemporary computational methods for solving major problems of current interest, from underwater sound scattering to space–time issues to aerodynamics
  • Describes the basic physics of the associated wave phenomena
  • Surveys state-of-the-art developments, such as the discretization of local absorbing boundary conditions and the perfectly matched layer technique
  • Includes applications of waves in compressible fluids and nonlinear dispersive, acoustic, elastic, and seismic waves

  • Summary

    Due to the increase in computational power and new discoveries in propagation phenomena for linear and nonlinear waves, the area of computational wave propagation has become more significant in recent years. Exploring the latest developments in the field, Effective Computational Methods for Wave Propagation presents several modern, valuable computational methods used to describe wave propagation phenomena in selected areas of physics and technology.

    Featuring contributions from internationally known experts, the book is divided into four parts. It begins with the simulation of nonlinear dispersive waves from nonlinear optics and the theory and numerical analysis of Boussinesq systems. The next section focuses on computational approaches, including a finite element method and parabolic equation techniques, for mathematical models of underwater sound propagation and scattering. The book then offers a comprehensive introduction to modern numerical methods for time-dependent elastic wave propagation. The final part supplies an overview of high-order, low diffusion numerical methods for complex, compressible flows of aerodynamics.

    Concentrating on physics and technology, this volume provides the necessary computational methods to effectively tackle the sources of problems that involve some type of wave motion.

    Table of Contents

    PREFACE
    Nonlinear Dispersive Waves
    Numerical Simulations of Singular Solutions of Nonlinear Schrödinger Equations
    Xiao-Ping Wang
    Numerical Solution of the Nonlinear Helmholtz Equation
    G. Fibich and S. Tsynkov
    Theory and Numerical Analysis of Boussinesq Systems: A Review
    V.A. Dougalis and D.E. Mitsotakis
    The Helmholtz Equation and its Paraxial Approximations in Underwater Acoustics
    Finite Element Discretization of the Helmholtz Equation in an Underwater Acoustic Waveguide
    D.A. Mitsoudis, N.A. Kampanis, and V.A. Dougalis
    Parabolic Equation Techniques in Underwater Acoustics
    D.J. Thomson and G.H. Brooke
    Numerical Solution of the Parabolic Equation in Range-Dependent Waveguides
    V.A. Dougalis, N.A. Kampanis, F. Sturm, and G.E. Zouraris
    Exact Boundary Conditions for Acoustic PE Modeling over an N2-Linear Half-Space
    T.W. Dawson, G.H. Brooke, and D.J. Thomson
    Numerical Methods for Elastic Wave Propagation
    Introduction and Orientation
    P. Joly
    The Mathematical Model for Elastic Wave Propagation
    P. Joly
    Finite Element Methods with Continuous Displacement
    P. Joly
    Finite Element Methods with Discontinuous Displacement
    P. Joly and C. Tsogka
    Fictitious Domains Methods for Wave Diffraction
    P. Joly and C. Tsogka
    Space–Time Mesh Refinement Methods
    G. Derveaux, P. Joly, and J. Rodríguez
    Numerical Methods for Treating Unbounded Media
    P. Joly and C. Tsogka
    Waves in Compressible Flows
    High-Order Accurate Space Discretization Methods for Computational Fluid Dynamics
    J.A. Ekaterinaris
    Governing Equations
    J.A. Ekaterinaris
    High-Order Finite-Difference Schemes
    J.A. Ekaterinaris
    ENO and WENO Schemes
    J.A. Ekaterinaris
    The Discontinuous Galerkin (DG) Method
    J.A. Ekaterinaris
    INDEX

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