Book123

    Free register and download UseNet downloader, then you can FREE Download from UseNet.

    Download without Limit " Science/Engineering LAttice gas cellular automata and Lattice Boltzmann models -An Introduction " from UseNet for FREE!

Lattice-gas cellular automata (LGCA)1 and even more lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of (nonlinear) partial differential equations. Each month several papers appear with new models, investigations of known models or methodically interesting applications. The field of lattice-gas cellular automata started almost out of the blue in 1986 with the by now famous paper of Frisch, Hasslacher and Pomeau. These authors showed, that a kind of billiard game with collisions that conserve mass and momentum, in the macroscopic limit leads to the Navier-Stokes equation when the underlying lattice possesses a sufficient (hexagonal in two dimensions) symmetry. A few years later lattice Boltzmann models arose as an offspring of LGCA. Their higher flexibility compared to LGCA led to artificial microscopic models for several nonlinear partial differential equations including the Navier-Stokes equation. I have followed the exciting development of both methods since 1989 and from time to time have given courses on this topic at the Department of Physics and Electrical Engineering at the University of Bremen (Germany). The present book is an extended version of my lecture manuscript. The word `introduction' in the title implies two things. Firstly, the level of presentation should be appropriate for undergraduate students. Thus methods like the Chapman-Enskog expansion or the maximum entropy principle which are usually not taught in standard courses in physics or mathematics are discussed in some detail. Secondly, in an introduction many things have to be left out. This concerns, for instance, models with several colors which allow the simulation of multiphase flows3 or magneto hydrodynamics. Only a few applications of LGCA or LBM to physical problems can be considered. Interesting topics like the divergence of transport coefficients in 2D are not discussed. The interested reader will find, however, references pointing to original articles (especially in the `What else?' sections). The lattice-gas cellular automata require special programming techniques which are only sparsely discussed in the widely scattered literature. The book will hopefully fill a gap in this respect (see Subsections 3.1.2, 3.1.4, 3.2.2).Several program codes will be made available via internet Buy It at Lowest Price on Amazon

). Many mathematical text books and courses contain lots of definitions, theorems and proofs - and not much else. In this respect The current book is rather `unplugged': the emphasis is more focused on presenting the main Principles and not on teaching proof techniques. Nonetheless the proofs of several essential theorems are presented in detail.Last but not least, I would like to add a few comments on the exercises. Problems with one star (_) should be very easy to solve (in a few minutes); those with two stars require more thinking or somewhat lengthy (`... after some algebra ...') calculations. Exercises with three stars are very different. Some of them require quite a bit of programming; others address more advanced stu_which has not been treated here. And finally, some of the three star exercises point to open problems which I have not solved myself.

.

"

Rating:
2.5 out of 5 by Book123