1st Edition

Lecture Notes on Numerical Methods for Hyperbolic Equations




ISBN 9780415683883
Published April 30, 2012 by CRC Press
144 Pages

USD $180.00

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Book Description

This volume contains the lecture notes of the Short Course on Numerical Methods for Hyperbolic Equations (Faculty of Mathematics, University of Santiago de Compostela, Spain, 2-4 July 2011). The course was organized in recognition of Prof. Eleuterio Toro’s contribution to education and training on numerical methods for partial differential equations and was organized prior to the International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications, which honours Professor Toro in the month of his 65th birthday. These lecture notes on selected topics in numerical methods for hyperbolic equations are from renowned academics in both theoretical and applied fields, and include contributions on:

  • Nonlinear hyperbolic conservation laws
  • First order schemes for the Euler equations                                                                               
  • High-order accuracy: monotonicity and non-linear methods                                             
  • High-order schemes for multidimensional hyperbolic problems                                       
  • A numerical method for the simulation of turbulent mixing and its basis in mathematical theory

Lectures Notes on Numerical Methods for Hyperbolic Equations is intended primarily for research students and post-doctoral research fellows. Some background knowledge on the basics of the theoretical aspects of the partial differential equations, their physical meaning and discretization methods is assumed. 

Table of Contents

Foreword

Preface

Scientific committee of the short course

Nonlinear hyperbolic conservation laws—a brief informal introduction, S. Karni

First order schemes for the Euler equations, R. Abgrall

High-order accuracy: Monotonicity and non-linear methods, E.F. Toro

High-order schemes for multidimensional hyperbolic problems, M. Dumbser

A numerical method for the simulation of turbulent mixing and its basis in mathematical theory, T. Kaman, H. Lim, Y. Yu, D. Wang, Y. Hu, J.-D. Kim, Y. Li, L. Wu, J. Glimm, X. Jiao, X.-L. Li & R. Samulyak

Author index

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Reviews

'The Short Course you are organizing not only matches perfectly well the problems I am trying to address in my PhD but also provides a unique opportunity to look at these challenges from the point of view of world class leaders in the field of hyperbolic equations.' - A. Warzynski, University of Leeds, UK