Computational gasdynamics. (English) Zbl 0947.76001

Laney, Culbert B.

Cambridge: Cambridge University Press. xiv, 613 p. (1998).

This comprehensive book with a quite general title is, in fact, restricted to finite difference and finite volume methods applied to high-speed gas flows, especially to gas flows with shocks and steep gradients. The intended readership includes senior and graduate-level students in aerospace engineering as well as practising engineers who specialize in the computational fluid mechanics. The book is to a great extend self-contained and self-teaching (due to numerous problems concluding each chapter), and can also be used by experts as a reference book owing to extensive citations to the related topics.
The book is organized in five parts. The first two parts (“Gasdynamics review” and “Computational review”) are introductory and make the reader familiar with fundamentals of gas dynamics and numerical mathematics. Part III “Basic principles of computational gas dynamics” combines the material described in parts I and II. The author introduces here such important notions as conservation, the CFL condition, artificial viscosity, numerical stability and upwinding. The last two parts (“Basic and advanced methods of computational gas dynamics”) cover the numerical techniques at the next levels of sophistication, which the author defines as “first-generation” methods (Lax-Friedrichs, Lax-Wendroff, MacCormack’s and Godunov mehods), and “solution-sensitive” methods (TVD, ENO, flux-limited and flux-corrected methods).
The following chapter headings reflect in detail the material covered in the book: 1. Introduction; Part I. 2. Governing equations of gas dynamics; 2. Waves; 4. Scalar conservation laws; 5. The Riemann problem. Part II. 6. Numerical error; 7. Orthogonal functions; 8. Interpolation; 9. Piecewise-polynomial reconstruction; 10. Numerical calculus. Part III. 11. Conservation laws and other basic principles; 12. The CFL condition; 13. Upwind and adaptive stencils; 14. Artificial viscosity; 15. Linear stability; 16. Nonlinear stability. Part IV. 17. Basic numerical methods for scalar conservation laws; 18. Basic numerical methods for the Euler equations; 19. Boundary treatment. Part V. 20. Flux averaging I: Flux-limited methods; 21. Flux averaging II: Flux-corrected methods; 22. Flux averaging III: Self-adjusting hybrid methods; 23. Solution averaging: Reconstruction-evolution methods; 24. A brief introduction to multi-dimensions. A detailed subject index concludes the book.
On balance, this is a very useful monograph which should certainly be of interest to those dealing with finite difference and finite volume methods in computational fluid dynamics.

Reviewer: O.Titow (Berlin)

MSC:

76-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics
76M20	Finite difference methods applied to problems in fluid mechanics
76M12	Finite volume methods applied to problems in fluid mechanics
76N15	Gas dynamics (general theory)

Keywords:

finite difference method; finite volume method; Lax-Friedrichs method; Lax-Wendroff method; Godunov method; MacCormack’s method; shock wave; TVD schemes; ENO schemes; scalar conservation; piecewise-polynomial reconstruction; flux averaging; flux-limited methods; reconstruction-evolution methods; CFL condition; artificial viscosity; numerical stability; upwinding; flux-corrected methods; Riemann problem; Euler equations