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**Mathematics of large eddy simulation of turbulent flows.**
*(English)*
Zbl 1089.76002

Scientific Computation. Berlin: Springer (ISBN 3-540-26316-0/hbk). xvii, 348 p. (2006).

The rough contents of this monograph are as follows: Ch. 1. Introduction; Ch. 2. The Navier-Stokes equations; Ch. 3. Introduction to eddy viscosity models; Ch. 4. Improved eddy viscosity models; Ch. 5. Uncertainities in eddy viscosity models and improved estimates of turbulent flow functionals; Ch. 6. Basic criteria for subfilter-scale models; Ch. 7. Closure based on wavenumber asymtotics; Ch. 8. Scale similarity models; Ch. 9. Filtering on bounded domains; Ch. 10. Near-wall models in LES; Ch. 11. Variational approximation of LES models, and Ch. 12. Test problems for LES. The work also contains a subject index and 320 references.

According to the authors, “Large eddy simulation, LES, is about approximating local, spatial averages of turbulent flows”. In other words, “LES seeks to calculate the large, energetic structures in a turbulent flow”. The authors accomplish this aim with a reasonable balance between the physics of fluids and the mathematical (abstract) theory of Navier-Stokes equations. A particular attention is paid to near-wall model in LES, and a large variety of numerical simulations are carried out. The book addresses to graduate students as well as to a broad class of researchers with a basic knowledge of fundamental fluid dynamics. It is elegantly structured with clear and precise statements, and the graphical material is suggestive.

According to the authors, “Large eddy simulation, LES, is about approximating local, spatial averages of turbulent flows”. In other words, “LES seeks to calculate the large, energetic structures in a turbulent flow”. The authors accomplish this aim with a reasonable balance between the physics of fluids and the mathematical (abstract) theory of Navier-Stokes equations. A particular attention is paid to near-wall model in LES, and a large variety of numerical simulations are carried out. The book addresses to graduate students as well as to a broad class of researchers with a basic knowledge of fundamental fluid dynamics. It is elegantly structured with clear and precise statements, and the graphical material is suggestive.

Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca)