Direct numerical simulation results for a range of relative dispersion statistics over Taylor-scale Reynolds numbers up to 650 are presented in an attempt to observe and quantify inertial subrange scaling and, in particular, Richardson's t 3 law. The analysis includes the mean-square separation and a range of important but less-studied differential statistics for which the motion is defined relative to that at time t = 0. It seeks to unambiguously identify and quantify the Richardson scaling by demonstrating convergence with both the Reynolds number and initial separation. According to these criteria, the standard compensated plots for these statistics in inertial subrange scaling show clear evidence of a Richardson range but with an imprecise estimate for the Richardson constant. A modified version of the cube-root plots introduced by Ott and Mann ͓J. Fluid Mech. 422, 207 ͑2000͔͒ confirms such convergence. It has been used to yield more precise estimates for Richardson's constant g which decrease with Taylor-scale Reynolds numbers over the range of 140-650. Extrapolation to the large Reynolds number limit gives an asymptotic value for Richardson's constant in the range g = 0.55-0.57, depending on the functional form used to make the extrapolation.

The evolution in size and shape of three and four-particle clusters (triangles and tetrads, respectively) in isotropic turbulence is studied using direct numerical simulations at grid resolution up to 4096 3 and Taylor-scale Reynolds numbers from 140 to 1000. A key issue is the attainment of inertial range behavior at high Reynolds number, while the small-and large-time limits of ballistic and diffusive regimes, respectively, are also considered in some detail. Tetrad size expressed by the volume (V) and (more appropriately) the gyration radius (R) is shown to display inertial range scaling consistent with a Richardson constant close to 0.56 for two-particle relative dispersion. For tetrads of initial size in a suitable range moments of shape parameters, including the ratio V 2=3 =R 2 and normalized eigenvalues of a moment-of-inertia-like dispersion tensor, show a regime of near-constancy which is identified with inertial-range scaling. Sheet-like structures are dominant in this period, while pancakes and needles are more prevalent at later times. For triangles taken from different faces of each tetrad effects of the initial shape (isosceles right-angled or equilateral) are retained only for about one Batchelor time scale. In the inertial range there is a prevalence of nearly isosceles triangles of two long sides and one short side, representing one particle moving away from the other two which are still close together. In general, measures of shape display asymptotic scaling ranges more readily than measures of size. With some caveats, the simulation results are also compared with the limited literature available for multiparticle cluster dispersion in turbulent flow.

CMT-nek is a new scientific application for performing high fidelity predictive simulations of particle laden explosively dispersed turbulent flows. CMT-nek involves detailed simulations, is compute intensive and is targeted to be deployed on exascale platforms. The moving particles are the main source of load imbalance as the application is executed on parallel processors. In a demonstration problem, all the particles are initially in a closed container until a detonation occurs and the particles move apart. If all processors get an equal share of the fluid domain, then only some of the processors get sections of the domain that are initially laden with particles, leading to disparate load on the processors. In order to eliminate load imbalance in different processors and to speedup the makespan, we present different load balancing algorithms for CMT-nek on large scale multi-core platforms consisting of hundred of thousands of cores. The detailed process of the load balancing algorithms are presented. The performance of the different load balancing algorithms are compared and the associated overheads are analyzed. Evaluations on the application with and without load balancing are conducted and these show that with load balancing, simulation time becomes faster by a factor of up to 9.97.

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