The field of computational fluid dynamics (CFD) has matured since the au thor was first introduced to electronic computation in the mid-sixties. The progress of numerical methods has paralleled that of computer technology and software. Simulations are used routinely in all branches of engineering as a very powerful means for understanding complex systems and, ultimately, improve their design for better efficiency. Today's engineers must be capable of using the large simulation codes available in industry, and apply them to their specific problem by implemen ting new boundary conditions or modifying existing ones. The objective of this book is to give the reader the basis for understanding the way numerical schemes achieve accurate and stable simulations of phy sical phenomena, governed by equations that are related, yet simpler, than the equations they need to solve. The model problems presented here are linear, in most cases, and represent the propagation of waves in a medium, the diffusion of heat in a slab, and the equilibrium of a membrane under distributed loads. Yet, regardless of the origin of the problem, the partial differential equations (PDE's) reflect the physical phenomena to be modeled and can be classified as being of hyperbolic, parabolic or elliptic type. The numerical treatment depends on the equation type that can represent several physical situations as diverse as heat conduction and viscous fluid flow. Non linear model problems are also presented and solved, such as the transonic small disturbance equation and the equations of gas dynamics.

The concise style and the idea of making extensive use of carefully selected problems raises this book to a unique text for students as well as practitioners in numerical simulations of physical phenomena Includes supplementary material: sn.pub/extras

Klappentext
This textbook is written for senior undergraduate and graduate students as well as engineers who will develop or use code in the simulation of fluid flows or other physical phenomena. The objective of the book is to give the reader the basis for understanding the way numerical schemes achieve accurate and stable simulations of physical phenomena. It is based on the finite-difference method and simple enough problems that allow also the analytic solutions to be worked out. ODEs as well as hyperbolic, parabolic and elliptic types are treated. The reader also will find a chapter on the techniques of linearization of nonlinear problems. The final chapter applies the material to the equations of gas dynamics. The book builds on simple model equations and, pedagogically, on a host of problems given together with their solutions.

Inhalt

1. Introduction.- 2. Basics of the Finite-Difference Method.- 3. Application to the Integration of Ordinary Differential Equations.- 4. Partial Differential Equations.- 5. Integration of a Linear Hyperbolic Equation.- 6. Integration of a Linear Parabolic Equation.- 7. Integration of a Linear Elliptic Equation.- 8. Finite Difference Scheme for a Convection-Diffusion Equation.- 9. The Method of Murman and Cole.- 10. Treatment of Non-Linearities.- 11. Application to a System of Equations.- A. Problems.- B. Solutions to Problems.- References.