Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

介绍了Kirk—Othmer Encyclopedia of Chemical Technology（化工技术百科全书）（第五版）电子图书网络版数据库，并对该数据库使用方法和检索途径作出了说明，且结合实例简单地介绍了该数据库的检索方法。

Kirk-Othmer Encyclopedia of Chemical Technology数据库介绍及实例

An immersed boundary method with direct forcing for the simulation of particulate flows

The Maxwell-Stefan approach to mass transfer

Discrete particle simulation of particulate systems: A review of major applications and findings

Meso-scale structures that take the form of clusters and streamers are commonly observed in dilute gas–particle flows, such as those encountered in risers. Continuum equations for gas–particle flows, coupled with constitutive equations for particle-phase stress deduced from kinetic theory of granular materials, can capture the formation of such meso-scale structures. These structures arise as a result of an inertial instability associated with the relative motion between the gas and particle phases, and an instability due to damping of the fluctuating motion of particles by the interstitial fluid and inelastic collisions between particles. It is demonstrated that the meso-scale structures are too small, and hence too expensive, to be resolved completely in simulation of gas–particle flows in large process vessels. At the same time, failure to resolve completely the meso-scale structures in a simulation leads to grossly inaccurate estimates of inter-phase drag, production/dissipation of pseudo-thermal energy associated with particle fluctuations, the effective particle-phase pressure and the effective viscosities. It is established that coarse-grid simulation of gas–particle flows must include sub-grid models, to account for the effects of the unresolved meso-scale structures. An approach to developing a plausible sub-grid model is proposed.

The role of meso-scale structures in rapid gas–solid flows

Starting from a kinetic theory based two-fluid model for gas-particle flows, we first construct filtered two-fluid model equations that average over small scale inhomogeneities that we do not wish to resolve in numerical simulations. We then outline a procedure to extract constitutive models for these filtered two-fluid models through highly resolved simulations of the kinetic theory based model equations in periodic domains. Two- and three-dimensional simulations show that the closure relations for the filtered two-fluid models manifest a definite and systematic dependence on the filter size. Linear stability analysis of the filtered two-fluid model equations reveals that filtering does indeed remove small scale structures that are afforded by the microscopic twofluid model. 2008 American Institute of Chemical Engineers AIChE J, 54: 1431–1448, 2008

Filtered two‐fluid models for fluidized gas‐particle suspensions

Analysis of a frictional-kinetic model for gas-particle flow

Numerical models of gas-fluidized beds have become an important tool in the design and scale up of gas-solid chemical reactors. However, a single numerical model which includes the solid-solid and solid-fluid interaction in full detail is not feasible for industrial-scale equipment, and for this reason one has to resort to a multiscale approach. The idea is that gas-solid flow is described by a hierarchy of models at different length scales, where the particle-particle and fluid-particle interactions are taken into account with different levels of detail. The results and insights obtained from the more fundamental models are used to develop closure laws to feed continuum models which can be used to compute the flow structures on a much larger (engineering) scale. Our multi-scale approach involves the lattice Boltzmann model, the discrete particle model, and the continuum model based on the kinetic theory of granular flow. In this chapter we give a detailed account of each of these models as they are employed at the University of Twente, accompanied by some illustrative computational results. Finally, we discuss two promising approaches for modeling industrial-size gas-fluidized beds, which are currently being explored independently at the Princeton University and the University of Twente.

Multiscale modeling of gas-fluidized beds

Continuum model equations for unsteady gas-particle flows in devices such as fluidized beds and circulating fluidized bed risers contain unstable modes whose length scale is of the order of 10 particle diameters. Yet, because of limited computational resources, these flows are routinely simulated by solving the discretized version of continuum models over coarse spatial grids. These simulations resolve the large-scale flow structures but not the finer scale structures. In most industrial applications involving large devices, it is impractical to resolve all the fine-scale structures, and therefore the effects of the unresolved structures must be addressed through suitable subgrid models. Using gas-particle flows in a wide and very tall vertical channel as an example, we have demonstrated in this study that the results obtained in coarse-grid integration of the microscopic equations for gas-particle flows change appreciably if subgrid corrections to account for the effects of unresolved structures are incl...

Sankaran Sundaresan

Papers

The role of meso-scale structures in rapid gas–solid flows

Filtered two‐fluid models for fluidized gas‐particle suspensions

Analysis of a frictional-kinetic model for gas-particle flow

Multiscale modeling of gas-fluidized beds

Coarse-Grid Simulation of Gas-Particle Flows in Vertical Risers