Numerical Methods For Wave Propagation

In May 1995 a meeting took place at the Manchester Metropolitan Uni versity, UK, with the title International Workshop on Numerical Methods for Wave Propagation Phenomena. The Workshop, which was attended by 60 scientists from 13 countries, was preceded by a short course enti tled High-Resolution Numerical Methods for Wave Propagation Phenom ena. The course participants could then join the Workshop and listen to discussions of the latest work in the field led by experts responsible for such developments. The present volume contains written versions of their contributions from the majority of the speakers at the Workshop. Professor Amiram Harten, but for his untimely death at the age of 50 years, would have been one of the speakers at the Workshop. His remarkable contributions to Numerical Analysis of Conservation Laws are commemo rated in this volume, which includes the text of the First Harten Memorial Lecture, delivered by Professor P. L. Roe from the University of Michigan in Ann Arbour, USA.

This book surveys analytical and numerical techniques appropriate to the description of fluid motion with an emphasis on the most widely used techniques exhibiting the best performance. Analytical and numerical solutions to hyperbolic systems of wave equations are the primary focus of the book. In addition, many interesting wave phenomena in fluids are considered using examples such as acoustic waves, the emission of air pollutants, magnetohydrodynamic waves in the solar corona, solar wind interaction with the planet venus, and ion-acoustic solitons. Contents:Mathematical Description of FluidsLinear WavesModel Equations for Weakly Nonlinear WavesAnalytical Methods for Solving the Classical Model Wave EquationsNumerical Methods for a Scalar Hyperbolic EquationsReview of Numerical Methods for Model Wave EquationsNumerical Schemes for a System of One-Dimensional Hyperbolic EquationsA Hyperbolic System of Two-Dimensional EquationsNumerical Methods for the MHD EquationsNumerical Experiments Readership: Researchers in applied and pure mathematics as well as computational and mathematical physics. Keywords:Reviews:“This book tries to fill the gap in the literature by considering together analytical and numerical approaches. The main attention is paid to the wave solutions of the quasi-hyperbolic systems appearing in fluids, plasma, and astrophysics, taking into account the nonlinearity, dispersion, dissipation and randomness of media … It can be useful for students studying the modeling of the wave processes in fluids, plasma and astrophysics.”Professor Efim Pelinovsky Russian Academy of Sciences “The book will be of interest to readers intending to enter this field, and it contains an extensive bibliography that will be useful for readers wishing to widen their study of these topics.”Mathematics Abstracts “I found the book to be very thorough in its description of methods, and the difficulties faced in solving hyperbolic problems … overall I was impressed with this book, and I recommend it as an excellent review source.”Mathematical Reviews

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

This second edition with four additional chapters presents the physical principles and solution techniques for transient propagation in fluid mechanics and hydraulics. The application domains vary including contaminant transport with or without sorption, the motion of immiscible hydrocarbons in aquifers, pipe transients, open channel and shallow water flow, and compressible gas dynamics. The mathematical formulation is covered from the angle of conservation laws, with an emphasis on multidimensional problems and discontinuous flows, such as steep fronts and shock waves. Finite difference-, finite volume- and finite element-based numerical methods (including discontinuous Galerkin techniques) are covered and applied to various physical fields. Additional chapters include the treatment of geometric source terms, as well as direct and adjoint sensitivity modeling for hyperbolic conservation laws. A concluding chapter is devoted to practical recommendations to the modeler. Application exercises with on-line solutions are proposed at the end of the chapters.

The decades following SEG's 1990 volume on numerical modeling showed a step change in the application and use of full wave equation modeling methods enabled by the increase in computational power. Full waveform inversion, reverse time migration, and 3D elastic finite-difference synthetic data generation are examples. A searchable CD is included.

Covering a wide range of techniques, this book describes methods for the solution of partial differential equations which govern wave propagation and are used in modeling atmospheric and oceanic flows. The presentation establishes a concrete link between theory and practice.

"To my knowledge [this] is the first book to address specifically the use of high-order discretizations in the time domain to solve wave equations. [...] I recommend the book for its clear and cogent coverage of the material selected by its author." --Physics Today, March 2003

Provides scientists and engineers with a tool for accurate assessment of diffraction and ducting on radio and radar systems. The author gives the mathematical background to parabolic equations modeling and describes simple parabolic equation algorithms before progressing to more advanced topics such as domain truncation, the treatment of impedance boundaries, and the implementation of very fast hybrid methods combining ray-tracing and parabolic equation techniques. The last three chapters are devoted to scattering problems, with application to propagation in urban environments and to radar-cross- section computation. Annotation copyrighted by Book News, Inc., Portland, OR