Research Directions in Computational Mechanics (1991) / Chapter Skim
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13 Non-Linear Dynamics of Multiparticle Systems
13 Non-Linear Dynamics of Multiparticle Systems
Pages 122-130
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From page 122... ...
Advances in the basic science could provide significant economic benefits to a wide variety of energy and mineral recovery industries and other technologies utilizing or producing solid materials. Recent years have seen a vigorous growth of activity in computer simulation of multiparticle systems by direct solution of the underlying equations of motion that, because of the inherent nonlinearity and numerous degrees of freedom, are otherwise mathematically intractable.
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From page 123... ...
Computational simulations on idealized particle systems offer a relatively direct method to test, improve, or reject continuum models before undertaking much more costly and difficult experimental measurements on real systems. Also, with computer simulation many detailed properties of idealized systems can be "observed" that are virtually inaccessible to direct experimental measurement.
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From page 124... ...
While numerous quantities may be computed directly, one may also attempt to extract continuum constitutive relations and then switch to a continuum description for actual applications. This approach, often desirable because of the relatively small number of particles that can be monitored by direct integration of the Newtonian equations, has led to new continuum models for granular materials based on concepts from dense-gas kinetic theory.
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From page 125... ...
Source: After O Walton, 198S, Energy and Technology Review, Lawrence Livermore National Laboratory, Report UCRL-52000-~-9, Livermore, CA)
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From page 126... ...
Walton, 1988, Energy and Technology Review, Lawrence Livermore National Laboratory, Report UCRL-52000-88-9, Livermore, CA)
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From page 127... ...
, has recently been introducedi5 to allow for explicit tracking of the trajectories of millions of grains. For such particle-tracking methods, neither complex geometric boundaries nor explicit time dependence of flow poses great difficulty in the calculation, in contrast to the numerical solution of the corresponding continuum partial differential equations (when those are known)
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From page 128... ...
Unfortunately, no simple pairwise additive force rules are adequate to describe these interactions when the solid concentrations exceed more than a few volume percent, so there is an urgent need for novel computational methods. Stokesian Dynamics For particles suspended in viscous fluids at zero Reynolds number (Stokes)
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From page 129... ...
The computational efficiency of SD has been systematically improved over the past couple of years, and periodic cells containing upwards of a hundred particles can now be treated. To improve efficiency, the method has been modified to include the effects of short-range lubrication forces between nearest-neighbor particles as separate, pairwise forces, significantly reducing computational effort in the hi~hconcentration regime.
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From page 130... ...
The significant improvements in efficiency and realism of these new LGM fluid simulations and their inherent applicability to a much wider range of problems suggest that much future effort should be concentrated on further development and application to particulate suspensions. One exciting aspect of the lattice-gas approach is the prospect of simulating suspensions with about the same computational effort as that now used for dry granular solids by means of special very large-scale integrated (VLSI)
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