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Numerical simulation in fluid dynamics. A practical introduction. (English) Zbl 0945.76001

SIAM Monographs on Mathematical Modeling and Computation, 3. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. 217 p. (1997).
The authors provide insight into numerical simulation of fluid flows. In addition to the presentation of basic equations for laminar transient flows of viscous incompressible fluids, the authors describe simulation of free surface flows, energy and chemical transport, and turbulence. After a brief introduction to mathematical modelling in chapter 2, the central chapter 3 presents discretization of differential equations by finite differences, which is then applied to Navier-Stokes equations. A simple algorithm for the solution of the resulting discrete system of equations is also given. Chapter 4 provides some visualization techniques, while chapter 5 applies the described solution algorithms to standard problems from fluid dynamics (lid-driven cavity, flow over backward-facing step, pipe junction, and flow through complex geometries). After numerical simulation of some free boundary problems (chapter 6 and 7), the authors turn to parallelization techniques which enable to solve larger problems, and which at the same time accelerate the computations (chapter 8). An extension of previous mathematical models to thermal and turbulent flows, followed by the discretization of new equations, is considered in chapters 9 and 10. Suggestions on extending the program to three space dimensions, accompanied by several simulation examples, are the subject of chapter 11. On the whole, the book can be a valuable instrument in the hands of mathematicians and engineers involved in computational fluid dynamics. It is well suited for cross-disciplinary and application-oriented training at the university level, as well as for practitioners giving them basic insight into computational fluid dynamics.

MSC:

76-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76M27 Visualization algorithms applied to problems in fluid mechanics
65Y05 Parallel numerical computation

Software:

GENSMAC; PLTMG; MPI
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