Effective Computational Methods for Wave Propagation

by Kampanis; Nikolaos A.

• ISBN13: 9781584885689
• ISBN10: 1584885688
• Edition: 1st
• Format: Hardcover
• Copyright: 2008-02-25
• Publisher: Chapman & Hall/

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 Propagationpresents 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 wavepropagation. 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

Nonlinear Dispersive Waves

Numerical Simulations of Singular Solutions of the Nonlinear

Numerical Solution of the Nonlinear Helmholtz Equation

Theory and numerical analysis of Boussinesq systems

A review

The Helmholtz Equation and its Paraxial Approximations in Underwater Acoustics

Finite element discretization of the Helmholtz equation in an underwater acoustic waveguide

Parabolic Equation Techniques in Underwater Acoustics

Numerical Solution of the Parabolic Equation in Range-Dependent Waveguides

Exact Boundary Conditions for Acoustic PE Modeling Over an N2-Linear Half-Space

Numerical Methods for Elastic Wave Propagation

Introduction and Orientation

The Mathematical Model for Elastic Wave Propagation

Finite Element Methods with Continuous Displacement

Finite Element Methods with Discontinuous Displacement

Fictitious Domains Methods for Wave Diffraction

Space Time Mesh Refinement Methods

Numerical Methods for Treating Unbounded Media

Waves In Compressible Flows

High-Order Accurate Space Discretization

Methods for Computational Fluid Dynamics

Governing Equations

High-Order Finite-Difference Schemes

ENO and WENO Schemes

The Discontinuous Galerkin (DG) Method

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