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Applied lattice Boltzmann method for transport phenomena, momentum, heat and mass transfer.

Applied Lattice Boltzmann Method for Transport Phenomena, Momentum, Heat and Mass Transfer.

A. A. Mohamad

Sure Printing, Calgary, AB April 2007

Over the last fifteen years the Lattice Boltzmann (LB) method has known an impressive expansion as an alternative computational technique for the numerical solution of complex fluid dynamic problems. This growth is witnessed by thousands of papers in the scientific literature and nearly two million google hits at the time of this writing. The LB is based on a paradigm shift as compared to standard computational fluid dynamics: rather than discretizing the partial differential equations of continuum fluid mechanics, LB goes back to the molecular roots of fluid motion, by tracing the dynamic evolution of the particle probability distribution function, as described by a suitably discretized Boltzmann kinetic equation. Here, suitably discretized, means that particles move along the links of a regular lattice, with a constant speed defined by the lattice links. Once on the same lattice site, they exchange mass, momentum and energy according to simple, local, collision rules. This paradigm shift, from continuum mechanics to (lattice) kinetic theory, brings about a series of major computational assets, primarily the fact that non-locality (particle streaming) is linear and non-linearity (particle collisions) is local. Most importantly, since particles move from one lattice site to another along straight trajectories, the streaming step can be performed exactly (zero-error) on a computer. At the same time, since collision rules have built-in mass and momentum energy conservation, such conservations are guaranteed up to machine round-off in computer implementations. Last but not least, the conceptual and mathematical transparence of the stream-collide dynamics translates into a corresponding computational efficiency and ease of implementation. Such simplicity lies at the heart of the great expansion of LB across virtually all fields of fluid-mechanics.

Despite the huge body of scientific literature, only a relatively few textbooks are available on the subject to date. The earliest one, by D. Wolf-Gladrow (Springer, 2000), deals with LB in conjunction with its historical ancestor, the Lattice-Gas Cellular Automata method and it is mostly addressed to a math-oriented audience. The first monograph entirely devoted to LB (S. Succi, Oxford U.P., 2001) appears to be penchee towards a physicist's audience. Subsequent books (Zhou, Springer, 2004; Sukop and Thorme, Springer, 2006) are wisely addressing only specific subfields of LB applications. Badly missing in this scenario was a book conveying the very basics of LB for warm-up engineering applications. Prof Mohamad's book is extremely timely in filling this major hole in the LB literature.

The book starts with a few elementary notions of kinetic theory, a notoriously hard subject for all but math-oriented readers. It then goes on with the basics of the Lattice Boltzmann method, again in the spirit of conveying just the very essential notions for an easy start-up on the subject. Subsequently, the cases of diffusion equations for mass, momentum and energy transfer are discussed by means of working examples. Here, the author draws nice and instructive parallels between LB and finite-difference methods which help a lot in fixing the ideas about relations and distinctions between the two approaches. Chapter IV extends these ideas to the case of advection-diffusion problems. Chapter V and VI deal with isothermal and non-isothermal incompressible fluid problems, respectively. Finally Chapter VII, on Complex Flows, is confined to a series of qualitative considerations on the potential advantages of the LB method over traditional CFD, for the tracking of complex and moving interfaces which occur in most multi-phase flows.

All of the hard-core chapters (III to VI), have a quite marked common structure: a few elementary theoretical notions, followed by concrete examples and ensuing computer listings. This latter feature sounds a bit 'demodee', but I think it is nonetheless much more useful, for didactical purposes, than the more common practice of relegating computer programs to appendices/floppy-disks, since it allows the reader to taste the simplicity of LB coding right away (eventually, C-language would have been a better choice for young readers, but that's a minor detail). The principle of simplicity which inspires this book throughout is indeed its major strength: those readers who get sufficient appetite, are then directed to more in-depth books/references through the final chapter, devoted to selected references.

Inevitably, this simplicity is also a liability in certain respects; for instance the discussion on discrete local equilibria could have been a bit less scanty without hampering, in my opinion, the aforementioned 'principle of simplicity'. On the same line, I feel that a few compact comments on the main LB limitations would have been useful; for instance, the fact that LB cannot deal with self-consistent thermohydrodynamics (local temperature coupling directly into the local equilibria) could have been mentioned, to warn the reader that fluid problems with strong compressibility and heat-release effects (e.g. internal engine combustion) are still unsuited to LB techniques. Finally, the text presents occasional typos and minor inaccuracies here and there that should be easily polished-up in future editions. All in all, I find Prof Mohammad's book a most welcome, timely and useful contribution to the didactical literature in the field. As I said, it nicely fills a big hole and successfully delivers on its charter statement "a textbook ... for engineers and for people willing to use the power of the method with little background in mathematics and physics". As a result, I feel like strongly recommending it to all beginners on the subject and even more so to all teachers in the field, including this reviewer. I already used it in a recent series of lectures: it works!

S. Succi

Istituto per le Applicazioni del Calcolo

"Mauro Picone" del C.N.R.,
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Author:Mohamad, A. A.
Publication:Canadian Journal of Chemical Engineering
Date:Dec 1, 2007
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