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

In this article the principles of the field operation and manipulation (FOAM) C++ class library for continuum mechanics are outlined. Our intention is to make it as easy as possible to develop reliable and efficient computational continuum-mechanics codes: this is achieved by making the top-level syntax of the code as close as possible to conventional mathematical notation for tensors and partial differential equations. Object-orientation techniques enable the creation of data types that closely mimic those of continuum mechanics, and the operator overloading possible in C++ allows normal mathematical symbols to be used for the basic operations. As an example, the implementation of various types of turbulence modeling in a FOAM computational-fluid-dynamics code is discussed, and calculations performed on a standard test case, that of flow around a square prism, are presented. To demonstrate the flexibility of the FOAM library, codes for solving structures and magnetohydrodynamics are also presented with appropriate test case results given. © 1998 American Institute of Physics.

A tensorial approach to computational continuum mechanics using object-oriented techniques

Supermassive black holes (BHs) have been found in 85 galaxies by dynamical modeling of spatially resolved kinematics. The Hubble Space Telescope revolutionized BH research by advancing the subject from its proof-of-concept phase into quantitative studies of BH demographics. Most influential was the discovery of a tight correlation between BH mass and the velocity dispersion σ of the bulge component of the host galaxy. Together with similar correlations with bulge luminosity and mass, this led to the widespread belief that BHs and bulges coevolve by regulating each other's growth. Conclusions based on one set of correlations from in brightest cluster ellipticals to in the smallest galaxies dominated BH work for more than a decade. New results are now replacing this simple story with a richer and more plausible picture in which BHs correlate differently with different galaxy components. A reasonable aim is to use this progress to refine our understanding of BH-galaxy coevolution. BHs with masses of 105−106M...

https://www.annualreviews.org/doi/suppl/10.1146/annurev-astro-082708-101811/suppl_file/aa51_kormendy_supmat.pdf

Coevolution (Or Not) of Supermassive Black Holes and Host Galaxies

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Inlet conditions for large eddy simulation: A review

Evolving cooling flows

Recently, a number of studies have indicated that Large Eddy Simulation (LES) models are fairly insensitive to the adopted Subgrid Scale (SGS) models. In order to study this and to gain further insight into LES, simulations of forced and decaying homogeneous isotropic turbulence have been performed for Taylor Re numbers between 35 and 248 using various SGS models, representative of the contemporary state of the art. The predictive capability of the LES concept is analyzed by comparison with DNS data and with results obtained from a theoretical model of the energy spectrum. The resolved flow is examined by visualizing the morphology and by analyzing the distribution of resolved enstrophy, rate of strain, stretching, SGS kinetic energy, and viscosity. Furthermore, the correlation between eigenvalues of the resolved rate of strain tensor and the vorticity is investigated. Although the gross features of the flow appear independent of the SGS model, pronounced differences between the models become apparent whe...

A comparative study of subgrid scale models in homogeneous isotropic turbulence

The necessity for turbulent combustion modeling in the large-eddy simulation (LES) of premixed turbulent combustion is evident from the computational cost and the complexity of handling flame kinetics reaction mechanisms directly. In this paper, a new flame-wrinkling LES combustion model using conditional filtering is proposed. The model represents an alternative approach to the traditional flame-surface density based models in that the flame distribution is represented by a flame-wrinkle density function and that the effects of flame stretch and curvature are handled through a modeled transport equation for the perturbed laminar flame speed. For the purpose of validating the LES combustion model, LESs of isothermal and reacting shear layers formed at a rearward-facing step are carried out, and the results are compared with experimental data. For the isothermal case, the agreement between LES and the experimental data is excellent. For the reacting case, the evolution and topology of coherent structures is examined, and direct comparisons are made with time-averaged profiles of velocity and its fluctuations. temperature, and reaction products. Good agreement is obtained, to a large extent due to accurate modeling of the flame-wrinkle density but also to the novel treatment of the strain-rate effects on the laminar flame speed of the lean propane-air mixture.

Gavin Tabor

Papers

A tensorial approach to computational continuum mechanics using object-oriented techniques

Inlet conditions for large eddy simulation: A review

Evolving cooling flows

A comparative study of subgrid scale models in homogeneous isotropic turbulence

Application of a flame-wrinkling les combustion model to a turbulent mixing layer