Three-Dimensional Simulations

We discuss, here, some examples of computational solutions to shock or impulsive loading problems. We consider, in turn, one-, two-, and three-dimensional simulations, and the role each typically plays in computational physics and mechanics investigations. 

Lam, K.Y., Cleary, M.P., and Barr, D.T. "A Complete Three-Dimensional Simulator for Analysis and Design of Hydraulic Fracturing," 1986 spe Unconventional Gas Technology Symposium, Louisville, May 18-21. 

Reaction-diffusion systems can readily be modeled in thin layers using CA. Since the transition rules are simple, increases in computational power allow one to add another dimension and run simulations at a speed that should permit the simulation of meaningful behavior in three dimensions. The Zaikin-Zhabotinsky reaction is normally followed in the laboratory by studying thin films. It is difficult to determine experimentally the processes occurring in all regions of a three-dimensional segment of excitable media, but three-dimensional simulations will offer an interesting window into the behavior of such systems in the bulk. 

In a three-dimensional simulation, a physical-space cube of volume V L (i.e., L in each direction) is employed. Thus, the total number of ODEs that must be solved scales as... 

A three-dimensional simulation method was used to simulate this extrusion process and others presented in this book. For this method, an FDM technique was used to solve the momentum equations Eqs. 7.43 to 7.45. The channel geometry used for this method was essentially identical to that of the unwound channel. That is, the width of the channel at the screw root was smaller than that at the barrel wall as forced by geometric constraints provided by Fig. 7.1. The Lagrangian reference frame transformation was used for all calculations, and thermal effects were included. The thermal effects were based on screw rotation. This three-dimensional simulation method was previously proven to predict accurately the simulation of pressures, temperatures, and rates for extruders of different diameters, screw designs, and resin types. 

Multidimensional thermal models were presented by many PEFC modeling groups. Maggio et al. performed the pseudo-three-dimensional simulations, neglecting the temperature gradient in the flow direction. However they only considered the overall heat source term as (Uo — In the three-... 

H. Takahashi, K. Tokunaga, T. Kasuga, and T. Suzuki, Modeling of Chemical Mechanical Polishing Process for Three-Dimensional Simulation, 1997 Symp. on VLSI Tech., pp. 25 26, Kyoto, Japan, 1997. 

Brasseur, G. P., X. Tie, P. J. Rasch, and F. Lefevre, A Three-Dimensional Simulation of the Antarctic Ozone Hole Impact of Anthropogenic Chlorine on the Lower Stratosphere and Upper Troposphere, J. Geophys. Res., 102, 8909-8930 (1997). 

Lu, R., and R. P. Turco, Ozone Distributions over the Los Angeles Basin Three-Dimensional Simulations with the Smog Model, Atmos. Environ., 30, 4155-4176 (1996). 

Advances in computer design and improved speed of numerical iteration to make three-dimensional simulation of macromolecules practical without crystallization of proteins. These simulations provide structural information about active sites, binding domains, or immunodominant sites, and confirmation. Integration of these advances allow structure-based and computed-aided drug design. 

Figure 5.6 Sample three-dimensional simulations of the IP process. (Top) Finite element mesh. Total length 30 cm (0 < X < 30), total height 1 cm (0 < Z < 1), total width 3 cm (0 < Y < 3). Fluid is injected from both sides through the thickness (i.e., in the Z-direction through a 1 cm x 1 cm square). (Bottom) Flow front progression at the midplane (i.e., Z — 0.5), Ka = Kzz = 2Kyy K, - = 0.0...

As a second example, results from fully three dimensional simulations of a 5 cell fuel cell stack performed using FLUENT s SOFC module are presented. The geo-... 

Balkanski, Y.J., D.J. Jacob, G.M. Gardner, W.C. Graustein, and K.K. Turekian. 1993. Transport and residence times of tropospheric aerosols inferred from a global three-dimensional simulation of 210Pb. /. Geophys. Res. 98 20573-20586. 

S, -W. Kim. Three-Dimensional Simulation for the Filling Stage of the Polymer Injection Molding Process Using the Finite Element Method. PhD thesis, University of Wisconsin-Madison, 2005. 

L.-S. Turng and S.-W. Kim. Three-dimensional simulation for the filling stage of the polymer injection molding process using the finite element method. To be published, 2005. 

Welch, S. and Rubini, P. Three-dimensional simulation of a fire-resistance furnace. In Hasemi, Y. (ed.). Proceedings of Fifth (5th) International Symposium on Fire Safety Science. March 3-7, Melbourne, Australia. Boston, MA International Association for Fire Safety Science, 1997, pp. 1009-1020. 

The formation of RES and their evolution into post-solitons have been observed in three-dimensional simulations as well [14], The EM structure of the three-dimensional soliton is such that the electric field is poloidal and the magnetic field is toroidal. Therefore it is named a TM-soliton. The soliton core is characterized by an overall positive charge, resulting in its Coulomb explosion and in the acceleration of the ion. On the long time-scale, the quasi-neutral plasma cavity is subject to a slow continuous radial expansion, while the soliton amplitude decreases and the ion temperature increases. 

This general technique was employed to simulate the motion of a mono-layer of identical spherical particles subjected to a simple shear. Confinement to a monolayer represents tremendous economies of computer time compared with a three-dimensional simulation. Hopefully, these highly specialized monolayer results will provide comparable insights into the physics of three-dimensional suspensions. Periodic boundary conditions were used in the simulation, and the method of Evans (1979) was incorporated to reproduce the imposed shear. 

A Web-Based Three-Dimensional Simulation System for Solute Transport in Soil... 

Three-Dimensional Simulation System and Related Technologies... 

With the development of the Internet, online access to scientific computing resources became possible. Diverse web technologies are used in this research to separately implement the one- and three-dimensional MRTM simulation systems. The web technologies used in the one-dimensional simulation system are discussed in Zeng et al. (2002). This section covers details of web technologies, especially Java technologies, that are used in the three-dimensional simulation system. The major goals and system requirements of the two simulation systems are also compared. 

Segol, G., Hopscotch algorithm for three-dimensional simulation, J. Hydraulic Eng., 118, 385, 1992. 

Further refinement of the flow models from Step 3 for adaptation into field-scale simulators and development of one-and three-dimensional simulators for eventual field project design. Phenomenological determinations by high-pressure experiments of dispersion properties required of sweep control surfactant systems and selection of homologous series of surfactants (42-45). 

De Saegher, J. J., Detemmerman, T., and Froment, G. E, Three dimensional simulation of high severity internally finned cracking coils for olefin production. Rev. Inst. Francois Du Pitrole 51(2), 245 (1996). 

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