involving shock waves that were of interest to the author. Accordingly, the reader is
strongly advised to consult the standard texts on fluid or gas dynamics for a
comprehensive account of fluid motion as well the rapidly growing area of CFD
by the experts in the area. Several textbooks and articles that I found useful can be
found in the references at the end of each chapter.
The book is suitable for both graduate and advanced undergraduate students in
applied mathematics, engineering and physics who are taking courses in fluid
dynamics and who require an introduction to a specific numerical technique for
dealing with shock waves. I decided very early on that the program listings would
not be included for the very good reason that there are good and bad programming
techniques and I would probably fall into the latter category. Nonetheless, the finite
difference representation of the differential equations is presented, and it is hoped
that this will be a starting point to encourage interested students to obtain solutions to
similar problems in compressible flow using their preferred programming language.
It is hoped that the material presented here will renew interest in gas dynamics and
shock waves in the undergraduate physics curriculum.
The book is structured in such a manner as to allow the reader to review some
basic material in relation to the equations of fluid flow. In this respect, a brief review
of the one-dimensional form of the equations is presented in Chap. 1 together with
the propagation of small amplitude disturbances. Chapter 1 also includes some basic
thermodynamic relationships that are relevant to gas dynamics. Waves of finite
amplitude and the formation of shock waves are discussed in Chap. 2. This chapter
also includes a basic introduction to the method of characteristics and to Riemann
invariants. Some important relationships arising from the conservation of mass,
momentum and energy across the shock front are presented in Chap. 3, and these
relationships are used in the subsequent chapters to ascertain the accuracy of the
numerical results obtained. Chapter 4 outlines the numerical procedure employed to
solve some examples of plane shock waves using artificial viscosity: The differential
equations in Lagrangian form are derived, and the corresponding difference equations are presented. Stability issues in relation to these equations are briefly
discussed as well as the choice of grid interval to be used in the numerical procedure.
Several simple examples of plane shocks arising from piston motion are also
presented and discussed. The remaining chapters deal with spherical shock waves:
Chap. 5 has an almost independent character and deals exclusively with the strongshock, point-source solution and its ramifications. Chapter 6 describes the numerical
procedure used when dealing with spherical shock waves, and the appropriate
differential equations in Lagrangian form are derived, and the difference form of
these equations incorporating artificial viscosity is presented. The equations are
numerically integrated to predict the pressure, density and particle velocity as
functions of position outside the strong-shock regime by using the strong-shock,
point-source solution as initial conditions. Finally, the shock waves generated
following the sudden expansion of a high-pressure, high-temperature sphere of air
into the surrounding atmosphere are presented and discussed.
viii
Preface to the First Edition
strongly advised to consult the standard texts on fluid or gas dynamics for a
comprehensive account of fluid motion as well the rapidly growing area of CFD
by the experts in the area. Several textbooks and articles that I found useful can be
found in the references at the end of each chapter.
The book is suitable for both graduate and advanced undergraduate students in
applied mathematics, engineering and physics who are taking courses in fluid
dynamics and who require an introduction to a specific numerical technique for
dealing with shock waves. I decided very early on that the program listings would
not be included for the very good reason that there are good and bad programming
techniques and I would probably fall into the latter category. Nonetheless, the finite
difference representation of the differential equations is presented, and it is hoped
that this will be a starting point to encourage interested students to obtain solutions to
similar problems in compressible flow using their preferred programming language.
It is hoped that the material presented here will renew interest in gas dynamics and
shock waves in the undergraduate physics curriculum.
The book is structured in such a manner as to allow the reader to review some
basic material in relation to the equations of fluid flow. In this respect, a brief review
of the one-dimensional form of the equations is presented in Chap. 1 together with
the propagation of small amplitude disturbances. Chapter 1 also includes some basic
thermodynamic relationships that are relevant to gas dynamics. Waves of finite
amplitude and the formation of shock waves are discussed in Chap. 2. This chapter
also includes a basic introduction to the method of characteristics and to Riemann
invariants. Some important relationships arising from the conservation of mass,
momentum and energy across the shock front are presented in Chap. 3, and these
relationships are used in the subsequent chapters to ascertain the accuracy of the
numerical results obtained. Chapter 4 outlines the numerical procedure employed to
solve some examples of plane shock waves using artificial viscosity: The differential
equations in Lagrangian form are derived, and the corresponding difference equations are presented. Stability issues in relation to these equations are briefly
discussed as well as the choice of grid interval to be used in the numerical procedure.
Several simple examples of plane shocks arising from piston motion are also
presented and discussed. The remaining chapters deal with spherical shock waves:
Chap. 5 has an almost independent character and deals exclusively with the strongshock, point-source solution and its ramifications. Chapter 6 describes the numerical
procedure used when dealing with spherical shock waves, and the appropriate
differential equations in Lagrangian form are derived, and the difference form of
these equations incorporating artificial viscosity is presented. The equations are
numerically integrated to predict the pressure, density and particle velocity as
functions of position outside the strong-shock regime by using the strong-shock,
point-source solution as initial conditions. Finally, the shock waves generated
following the sudden expansion of a high-pressure, high-temperature sphere of air
into the surrounding atmosphere are presented and discussed.
viii
Preface to the First Edition