zbMATH — the first resource for mathematics

Numerical computation of internal and external flows. Volume 2: Computational methods for inviscid and viscous flows. (English) Zbl 0742.76001
Wiley Series in Numerical Methods in Engineering. Chichester etc.: John Wiley & Sons,. xxi, 691 p. (1990).
While the first volume of this work ( Zbl 0662.76001) was devoted to the theory of numerical methods for the solution of partial differential equations occuring in fluid mechanics, the second volume is devoted to the description of a large number of finite difference schemes. The volume contains Part V: The numerical computation of potential flows, Part VI: The numerical solution of the system of Euler equations and Part VII: The numerical solution of the Navier-Stokes equations.
The first chapter in each of the parts contains a detailed mathematical description of the partial differential equations to be solved and of their properties. Important questions like possible boundary conditions, the use of conservative versus nonconservative formulations and turbulence models (for Part VII) are also included in these initial chapters. Approximately 2/3 of the book is devoted to the numerical solution of the compressible Euler equations. Starting with the description of finite difference schemes of the Lax-Wendroff family this part describes nearly every method in use today. The part ends with second-order upwind and high-resolution TVD schemes, so that latest developments like ENO schemes are not included. Part VII concerning the Navier-Stokes equations includes the description of methods for incompressible as well as for compressible flows. Like in the Euler part finite difference methods are discussed exclusively, though some references to the finite element literature are given. A small part of Part V is concerned with finite element methods in connection with potential flows.

MSC:
 76-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 76M20 Finite difference methods applied to problems in fluid mechanics