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

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

We present a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an infinite-dimensional linear operator associated with the full nonlinear system. These modes, referred to as Koopman modes, are associated with a particular observable, and may be determined directly from data (either numerical or experimental) using a variant of a standard Arnoldi method. They have an associated temporal frequency and growth rate and may be viewed as a nonlinear generalization of global eigenmodes of a linearized system. They provide an alternative to proper orthogonal decomposition, and in the case of periodic data the Koopman modes reduce to a discrete temporal Fourier transform. The Arnoldi method used for computations is identical to the dynamic mode decomposition recently proposed by Schmid & Sesterhenn (Sixty-First Annual Meeting of the APS Division of Fluid Dynamics, 2008), so dynamic mode decomposition can be thought of as an algorithm for finding Koopman modes. We illustrate the method on an example of a jet in crossflow, and show that the method captures the dominant frequencies and elucidates the associated spatial structures.

Spectral analysis of nonlinear flows

▪ Abstract We review the direct numerical simulation (DNS) of turbulent flows. We stress that DNS is a research tool, and not a brute-force solution to the Navier-Stokes equations for engineering problems. The wide range of scales in turbulent flows requires that care be taken in their numerical solution. We discuss related numerical issues such as boundary conditions and spatial and temporal discretization. Significant insight into turbulence physics has been gained from DNS of certain idealized flows that cannot be easily attained in the laboratory. We discuss some examples. Further, we illustrate the complementary nature of experiments and computations in turbulence research. Examples are provided where DNS data has been used to evaluate measurement accuracy. Finally, we consider how DNS has impacted turbulence modeling and provided further insight into the structure of turbulent boundary layers.

/pdf/direct-numerical-simulation-a-tool-in-turbulence-research-2a650vh1lf.pdf

DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research

Numerical Initial Value Problems in Ordinary Differential Equations

A numerical method for large-eddy simulation in complex geometries

It is common for jets of fluid to interact with crossflow. This article reviews our understanding of the physical behavior of this important class of flow in the incompressible and compressible regimes. Experiments have significantly increased in sophistication over the past few decades, and recent experiments provide data on turbulence quantities and scalar mixing. Quantitative data at high speeds are less common, and visualization still forms an important component in estimating penetration and mixing. Simulations have progressed from the Reynolds-averaged methodology to large-eddy and hybrid methodologies. There is a general consensus on the qualitative structure of the flow at low speeds; however, the flow structure at low-velocity ratios (jet speed/crossflow speed) might be fundamentally different from the common notion of shear-layer vortices, counter-rotating vortex pairs, wakes, and horseshoe vortices. Fluid in the near field is strongly accelerated, which affects the jet trajectory, entrainment, ...

The Interaction of Jets with Crossflow

This paper studies the trajectories and near field of round jets in crossflow. Incompressible direct numerical simulations are performed at velocity ratios of 1.5 and 5.7 and the effects of jet velocity profile and boundary layer thickness on the jet trajectory are examined. The ‘rd’ scaling used at present (Margason 1993) does not contain any information on these parameters, and trajectories scaled by rd do not collapse. The trajectory is strongly influenced by the near field which depends on both the jet velocity profile and the crossflow boundary layer. A length scale is proposed to describe the near field of the jet. An analytical expression is proposed for this length scale which is a measure of the relative inertia of the jet and the crossflow. Incorporating this length scale significantly improves the scaling of the trajectories.

Study of trajectories of jets in crossflow using direct numerical simulations

http://web.engr.oregonstate.edu/~sva/archive/apte_ijmf_plf03.pdf

Krishnan Mahesh

Papers

DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research

A numerical method for large-eddy simulation in complex geometries

The Interaction of Jets with Crossflow

Study of trajectories of jets in crossflow using direct numerical simulations

Large-eddy simulation of swirling particle-laden flows in a coaxial-jet combustor