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

Data Mining Practical Machine Learning Tools and Techniques

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales

We present a multi–purpose CFD–DEM framework to simulate coupled fluid–granular systems. The motion of the particles is resolved by means of the Discrete Element Method (DEM), and the Computational Fluid Dynamics (CFD) method is used to calculate the interstitial fluid flow. We first give a short overview over the DEM and CFD–DEM codes and implementations, followed by elaborating on the numerical schemes and implementation of the CFD–DEM coupling approach, which comprises two fundamentally different approaches, the unresolved CFD–DEM and the resolved CFD–DEM using an Immersed Boundary (IB) method. Both the DEM and the CFD–DEM approach are successfully tested against analytics as well as experimental data.

Models, algorithms and validation for opensource DEM and CFD-DEM

Influence of rolling friction on single spout fluidized bed simulation

Particle shape representation is a fundamental problem in the Discrete Element Method (DEM). Spherical particles with well known contact force models remain popular in DEM due to their relative simplicity in terms of ease of implementation and low computational cost. However, in real applications particles are mostly non-spherical, and more sophisticated particle shape models, like superquadric shape, must be introduced in DEM. The superquadric shape can be considered as an extension of spherical or ellipsoidal particles and can be used for modeling of spheres, ellipsoids, cylinder-like and box(dice)-like particles just varying five shape parameters. In this study we present an efficient C++ implementation of superquadric particles within the open-source and parallel DEM package LIGGGHTS. To reduce computational time several ideas are employed. In the particle–particle contact detection routine we use the minimum bounding spheres and the oriented bounding boxes to reduce the number of potential contact pairs. For the particle–wall contact an accurate analytical solution was found. We present all necessary mathematics for the contact detection and contact force calculation. The superquadric DEM code implementation was verified on test cases such as angle of repose and hopper/silo discharge. The simulation results are in good agreement with experimental data and are presented in this paper. We show adequacy of the superquadric shape model and robustness of the implemented superquadric DEM code.

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Efficient implementation of superquadric particles in Discrete Element Method within an open-source framework

Two different approaches to constitutive relations for filtered two-fluid models (TFM) of gas–solid flows are deduced. The first model (Model A) is derived using systematically filtered results obtained from a highly resolved simulation of a bubbling fluidized bed. The second model (Model B) stems from the assumption of the formation of subgrid heterogeneities inside the suspension phase of fluidized beds. These approaches for the unresolved terms appearing in the filtered TFM are, then, substantiated by the corresponding filtered data. Furthermore, the presented models are verified in the case of the bubbling fluidized bed used to generate the fine grid data. The numerical results obtained on coarse grids demonstrate that the computed bed hydrodynamics is in fairly good agreement with the highly resolved simulation. The results further show that the contribution from the unresolved frictional stresses is required to correctly predict the bubble rise velocity using coarse grids. © 2013 American Institute of Chemical Engineers AIChE J, 60: 839–854, 2014

Stefan Pirker

Papers

Models, algorithms and validation for opensource DEM and CFD-DEM

Influence of rolling friction on single spout fluidized bed simulation

Efficient implementation of superquadric particles in Discrete Element Method within an open-source framework

Filtered and heterogeneity‐based subgrid modifications for gas–solid drag and solid stresses in bubbling fluidized beds

A comprehensive frictional-kinetic model for gas–particle flows: Analysis of fluidized and moving bed regimes