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. 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. Index.
Nikolaos A. Kampanis, Vassilios A. Dougalis, John A. Ekaterinaris