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

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Turbulent dispersed multiphase flows are common in many engineering and environmental applications. The stochastic nature of both the carrier-phase turbulence and the dispersed-phase distribution makes the problem of turbulent dispersed multiphase flow far more complex than its single-phase counterpart. In this article we first review the current state-of-the-art experimental and computational techniques for turbulent dispersed multiphase flows, their strengths and limitations, and opportunities for the future. The review then focuses on three important aspects of turbulent dispersed multiphase flows: the preferential concentration of particles, droplets, and bubbles; the effect of turbulence on the coupling between the dispersed and carrier phases; and modulation of carrier-phase turbulence due to the presence of particles and bubbles.

Turbulent Dispersed Multiphase Flow

Preface 1.General Considerations 2.Basic Processes in Atomization 3.Drop Size Distributions of Sprays 4.Atomizers 5.Flow in Atomizers 6.Atomizer Performance 7.External Spray Charcteristics 8.Drop Evaporation 9.Drop Sizing Methods Index

Atomization and Sprays

Solution of population balance equations using the direct quadrature method of moments

This book presents the current state of the art in computational models for turbulent reacting flows, and analyzes carefully the strengths and weaknesses of the various techniques described The focus is on formulation of practical models as opposed to numerical issues arising from their solution A theoretical framework based on the one-point, one-time joint probability density function (PDF) is developed It is shown that all commonly employed models for turbulent reacting flows can be formulated in terms of the joint PDF of the chemical species and enthalpy Models based on direct closures for the chemical source term as well as transported PDF methods are covered in detail An introduction to the theory of turbulent and turbulent scalar transport is provided for completeness The book is aimed at chemical, mechanical, and aerospace engineers in academia and industry, as well as developers of computational fluid dynamics codes for reacting flows

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Computational Models for Turbulent Reacting Flows

Investigation of particulate systems often requires the solution of a population balance, which is a continuity statement written in terms of the number density function. In turn, the number density function is defined in terms of an internal coordinate (e.g., particle length, particle volume) and it generates integral and derivative terms. Different methods exist for numerically solving the population balance equation. For many processes of industrial significance, due to the strong coupling between particle interactions and fluid dynamics, the population balance must be solved as part of a computational fluid dynamics (CFD) simulation. Such an approach requires the addition of a large number of scalars and the associated transport equations. This increases the CPU time required for the simulation, and thus it is clear that it is very important to use as few scalars as possible. In this work the quadrature method of moments (QMOM) is used. The QMOM has already been validated for crystal growth and aggregation; here the method is extended to include breakage. QMOM performance is tested for 10 different cases in which the competition between aggregation and breakage leads to asymptotic solutions.

Quadrature method of moments for aggregation-breakage processes.

Although use of computational fluid dynamics (CFD) for simulating precipitation (and particulate systems in general) is becoming a standard approach, a number of issues still need to be addressed. One major problem is the computational expense of coupling a standard discretized population balance (DPB) with a CFD code, as this approach requires the solution of an intractably large number of transport equations. In this work the quadrature method of moments (QMOM) is tested for size-dependent growth and aggregation. The QMOM is validated by comparison with both Monte Carlo simulations and analytical solutions using several functional forms for the aggregation kernel. Moreover, model predictions are compared with a DPB to compare accuracy, computational time, and the number of scalars involved. Analysis of the relative performance of various methods for treating aggregation provides readers with useful information about the range of application and possible limitations.

Rodney O. Fox

Papers

Solution of population balance equations using the direct quadrature method of moments

Computational Models for Turbulent Reacting Flows

Quadrature method of moments for aggregation-breakage processes.

Quadrature method of moments for population‐balance equations

Mixing in a multi-inlet vortex mixer (MIVM) for flash nano-precipitation