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The lattice Boltzmann equation. For fluid dynamics and beyond. (English) Zbl 0990.76001
Numerical Mathematics and Scientific Computation. Oxford: Clarendon Press. xvi, 288 p. (2001).
This work deals with a version of Boltzmann equation explicitly designed to solve fluid dynamics problems. First, the author gives a detailed survey of lattice Boltzmann equations (LBE) and their applications to fluid dynamics. The next presentation is divided into three parts. Part I describes the basic theoretical background of LBE. Part II discusses a number of selected fluid dynamics applications (flows through porous media, flows past obstacles, turbulent flows). Finally, part III makes the reader familiar with shear and backless flows under various conditions, such as flows with chemical reactions and phase transitions, flows with suspended particles, polymer and quantum flows.
On balance, the book is addressed to a broad audience of scientists interested in the fluid dynamics of complex systems. The book also looks for future developments in related areas (material science, biology etc.) where the fluid motion plays an important role.

MSC:
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76M28 Particle methods and lattice-gas methods
76V05 Reaction effects in flows
76T20 Suspensions
76A25 Superfluids (classical aspects)
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