G.D. Doolen, Lattice Gas Methods for Partial Differential Equations. Addison-Wesley, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Subject classification. Fluid Mechanics 1. Introduction. In recent years, methods of the lattice gas automata (LGA) and the lattice Boltzmann equation (LBE) have become an alternative to conventional computational fluid dynamics (CFD) methods for various systems (see collections of papers [16], proceedings [7, 6] reviews [4, 14, 30] and monographs [38, 15] The lattice gas and lattice Boltzmann methods have been particularly successful in dealing with fluid flow applications involving complex fluids and complicated boundaries, such as multi component fluids through porous media [8, ....

G.D. DOOLEN, editor, Lattice Gas Methods for Partial Differential Equations, Addison-Wesley, New York, 1990.

....development during this time was the introduction of special hardware in the form of cellular automata machines [89] and massively parallel computers. These investigations set the stage for the development of lattice gases [32, 55] which have become a separate area of research in themselves [24, 25]. In addition to lattice gases, one of the largest areas of current interest in CA involves studies in complexity [66, 97] CA constitute a powerful paradigm for pattern formation and self organization, and nowhere is this more pronounced than in the study of artificial life [52, 53] Given the ....

....conservation may 51 also be imposed. The problem when designing a lattice gas is to specify a rule that yields the desired phenomena while maintaining the constraints. For example, in hydrodynamic applications, one is often interested in choosing collision rules which minimize viscosity [24, 25]. However in this case, the goal is just to demonstrate a reversible dynamics which generates a statistical force corresponding to an external scalar potential. The specific CA model treated in this chapter consists of a pair of two dimensional lattice gases that are coupled via interaction with ....

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Gary D. Doolen, editor. Lattice Gas Methods for Partial Differential Equations, volume 4 of Santa Fe Institute Studies in the Sciences of Complexity. AddisonWesley, Redwood City, California, 1990.

.... suitable for modeling actual hydrodynamics (see [27] for a tutorial) Recently, analogous results for three dimensional models have been obtained by a number of researchers[22] Lattice gases are rapidly beginning to encroach into modeling niches dominated until recently by differential equations[16,49]; their success in this role is chiefly due to the ease with which they can be made to satisfy local continuity equations, #13 as discussed below and, more leisurely, in [72,75] Let us consider the spacetime texture induced by a lattice gas such as HPP. #14 In Fig. 6, the arcs represent the ....

Doolen, Gary, et al. (ed.), Lattice-Gas Methods for Partial Differential Equations, Addison-Wesley (1990).

....of collision is considered: when exactly three particles collide with an angle of 120 degrees between each other, they bounce back (so that the momentum after collision is zero, as it was before collision) Figure 23 illustrates this rule. Several variants of the FHP model exist in the literature [3], including some with rest particles, like the FHP II and FHP III models. For the simplest case we are considering here, all interactions come from the two collision processes described above. For all other configurations (i.e those which are not obtained by rotations of the situations given in ....

....collision term Omega i , is to average the microdymanics of a given underlying cellular automata fluid and factorize it into a product of average quantities, as we did in section 3 to get the Boltzmann approximation. However, as one considers more sophisticated lattice gas fluid (like FHP III [3]) or 3D models [61] the collision term requires a very large number of floating point operations at each lattice site and time step. Even on a massively parallel computer, in which every cells are computed simultaneously, this may not be acceptable. The first solution to this problem is to ....

G. Doolen, editor. Lattice Gas Method for Partial Differential Equations. Addison-Wesley, 1990.

....automata (CA) are an idealization of a physical system in which space, time and the physical quantities (or state of the automaton) take only a finite set of values. Since they have been invented by von Neumann in the late 1940s, CAs has been applied to a large range of scientific problems [1 4]. A very important feature of CAs is that they provide simple models of complex systems. They exemplify the fact that a collective behavior can emerge from the sum of many simple components. Even if the basic and local interactions are perfectly known, it is possible that the global behavior of a ....

G. Doolen, editor. Lattice Gas Method for Partial Differential Equations. Addison-Wesley, 1990.

....behind obstacles. The resulting effect is a modification of the reaction patterns which can be as dramatic as their disappearance. 1 Introduction The lattice Boltzmann method is a numerical method developped for simulating hydrodynamics [1] that was derived from lattice gas automaton methods [3]. In these methods, particles propagate on a lattice with discrete velocities and collide on the lattice sites. The lattice Boltzmann method replaces the particles with particle densities, which are propagated according to the discrete velocities. The collision step is replaced by a relaxation of ....

Gary Doolen, editor. Lattice gas methods for partial differential equations, Redwood City, CA, 1990. Addison-Wesley.

....insertion at a random position) These unphysical moves are extremely efficient in propagating the system through configuration space, but they do not allow for a dynamic interpretion of the trajectory. A lattice scheme which does capture hydrodynamic behavior is the Lattice Boltzmann method[88, 89, 90, 91]. These methods have been devised as an effective numerical technique of computational fluid dynamics. The basic variables are the time dependent probability distributions f ff (x; t) of a velocity class ff on a lattice site x. This probability distribution is then updated in discrete time steps ....

G.D. Doolen (ed.), "Lattice Gas methods for Partial Differential Equations",AddisonWesley, Redwood Ciry, CA (1990).

.... suitable for modeling actual hydrodynamics (see [27] for a tutorial) Recently, analogous results for three dimensional models have been obtained by a number of researchers[22] Lattice gases are rapidly beginning to encroach into modeling niches dominated until recently by differential equations[16, 49]; their success in this role is chiefly due to the ease with which they can be made to satisfy local continuity equations, 13 as discussed below and, more leisurely, in [72, 75] f t x y a b c d a b c d Figure 6: Spacetime layout of the HPP gas. t x t 0 a b c d f Figure 7: Evenly spaced ....

Doolen, Gary, et al. (ed.), Lattice-Gas Methods for Partial Differential Equations, Addison-Wesley (1990).

....Navier Stokes equation, and thus suitable for modeling actual hydrodynamics (see [23] for a tutorial) This model started off the burgeoning scientific business of lattice gas hydrodynamics. Soon after, analogous results for three dimensional models were obtained by a number of researchers[20, 12]. The approach is able to provide both conceptual[42] and practical insight into more complex situations, such as multiphase fluids and flow in porous media[8] and dynamics that ride on the fluid flow, as in Fig. 15. 4 Molecular computers The smallest electronic devices of today, about 100nm ....

Doolen, Gary, et al. (ed.), Lattice-Gas Methods for Partial Differential Equations, Addison--Wesley (1990).

....decendents of early work on cellular logic arrays[25, 4] There is one kind of programming, however, that is particularly well suited to implementation on a physics like digital system; namely the simulation of physics itself. This is the class of problems for which our machine is optimized[16, 24, 6, 2, 20, 7]. The Figures in this section show some simple examples of CA models of physics run on a small prototype cam 8. This 8 node machine contains less memory and logic than its SPARCstation front end, and runs at 25 MHz. Figure 2a illustrates a sound pulse in a simple two dimensional lattice gas an ....

G. Doolen, et al. (ed.), Lattice-Gas Methods for Partial Differential Equations, Addison-Wesley (1990).

....LBM describe physical systems in terms of the motion of fictitious microscopic particles on a lattice. This method is inspired by the cellular automata modeling techniques[6, 7] and allows efficient simulations of many complex physical situations like fluid dynamics and reaction diffusion processes[8, 9, 10]. Thus, the TLM method is characterized by a simultaneous dynamics (all flux are updated at the same time) and a very simple numerical scheme. The interpretation of the dynamics in terms of flux (or flows) makes the boundary conditions easy to implement. As a result, the TLM method is a natural ....

G. Doolen, editor. Lattice gas method for partial differential equations. AddisonWesley, 1990.

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G.D. Doolen, Lattice Gas Methods for Partial Differential Equations. Addison-Wesley, 1990.

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G.D. Doolen, Lattice Gas Methods for Partial Differential Equations. Addison-Wesley, 1990.

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G. Doolen et. al., editor. Lattice Gas Methods for Partial Differential Equations, Santa Fe Institute studies in the sciences of complexity, Proceedings Vol. IV. Addison-Wesley, 1989.

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