Numerical Methods in Fluid Dynamics: Initial and Initial Boundary-Value Problems

Gary A. Sod

doi:10.1017/CBO9780511753138

Numerical Methods in Fluid Dynamics

Initial and Initial Boundary-Value Problems

Here is an introduction to numerical methods for partial differential equations with particular reference to those that are of importance in fluid dynamics. The author gives a thorough and rigorous treatment of the techniques, beginning with the classical methods and leading to a discussion of modern developments. For easier reading and use, many of the purely technical results and theorems are given separately from the main body of the text. The presentation is intended for graduate students in applied mathematics, engineering and physical sciences who have a basic knowledge of partial differential equations.

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Numerical Methods in Fluid Dynamics

Initial and Initial Boundary-Value Problems

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Preface
pp ix-x

Chapter I - Introduction
pp 1-20

Chapter II - Parabolic Equations
pp 21-142

Chapter III - Hyperbolic Equations
pp 143-268

Chapter IV - Hyperbolic Conservation Laws
pp 269-372

Chapter V - Stability in the Presence of Boundaries
pp 373-396

Appendices

A - The Kreiss Matrix Theorem and Its Consequences
pp 397-402

B - Kreiss' Stability Theorems for Dissipative Methods
pp 403-416

C - The Lax-Nirenberg Theorem and a Special Case
pp 417-426

D - Hyperbolic Equations with Discontinuous Initial Data
pp 427-444

Index
pp 445-446

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Numerical Methods in Fluid Dynamics

Initial and Initial Boundary-Value Problems

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