Parallel computation for Boltzmann equation simulation with Dynamic Discrete Ordinate Method (DDOM)

Hsu, Chin; Sin, Ka Fai; Chiang, S.W.

doi:10.1016/j.compfluid.2011.09.011

Cited by 3 publications

(4 citation statements)

References 18 publications

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“…Neither CUDA nor OpenMP can combine computer nodes, but MPI can. Hybridization between these parallelisms means various kinds of parallelization need to undertake the difficult task to be combined in parts into a determined form, and there have been several successes of the hybrid parallelization with CUDA [10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Effects of Easy Hybrid Parallelization with CUDA for OpenMX

Parq¹,

Sevre²,

Lee³

2014

IJCA

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A MPI-friendly density functional theory (DFT) source code was modified within hybrid parallelization including CUDA. The objective is to find out how simple conversions within the hybrid parallelization with mid-range GPUs affect DFT code not originally suitable to CUDA. Several rules of hybrid parallelization for numerical-atomic-orbital (NAO) DFT codes were settled. The test was performed on a magnetite material system with OpenMX code by utilizing a hardware system containing 2 Xeon E5606 CPUs and 2 Quadro 4000 GPUs. 3-way hybrid routines obtained a speedup of 7.55 while 2-way hybrid speedup by 10.94. GPUs with CUDA complement the efficiency of OpenMP and compensate CPUs' excessive competition within MPI.

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Section: Introductionmentioning

confidence: 99%

Effects of Easy Hybrid Parallelization with CUDA for OpenMX

Parq¹,

Sevre²,

Lee³

2014

IJCA

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Effects of Easy Hybrid Parallelization with CUDA for Numerical-Atomic-Orbital Density Functional Theory Calculation

Parq,

Sevre,

Lee

2014

Preprint

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We modified a MPI-friendly density functional theory (DFT) source code within hybrid parallelization including CUDA. Our objective is to find out how simple conversions within the hybrid parallelization with mid-range GPUs affect DFT code not originally suitable to CUDA. We settled several rules of hybrid parallelization for numerical-atomic-orbital (NAO) DFT codes. The test was performed on a magnetite material system with OpenMX code by utilizing a hardware system containing 2 Xeon E5606 CPUs and 2 Quadro 4000 GPUs. 3-way hybrid routines obtained a speedup of 7.55 while 2-way hybrid speedup by 10.94. GPUs with CUDA complement the efficiency of OpenMP and compensate CPUs' excessive competition within MPI.

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“…This method is of some interest for near equilibrium ows, but not for rare ed conditions, as the author states the method will encounter error on the order of Knudsen number [101].…”

Section: Velocity Space Discretizationmentioning

confidence: 99%

“…A somewhat di erent approach, as introduced by Hsu et al [101], is to transform the distribution function into a form that is independent of mean velocity and temperature and thereby reduce the number of Gauss-Hermite quadrature points required for the same degree of accuracy. This method is of some interest for near equilibrium ows, but not for rare ed conditions, as the author states the method will encounter error on the order of Knudsen number [101].…”

Section: Velocity Space Discretizationmentioning

confidence: 99%

Numerical investigation of gaseous heat and mass transfer: the effect of rarefaction

Bond¹

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Recent advances in micro-scale fabrication have uncovered the limitations of classical uid dynamics analysis techniques. The current status of numerical techniques for micro-ows is found to be highly varied with no accepted best-practice. This situation encourages investigation of new and improved methods in the eld. In this work a new numerical method based upon the solution of the model Boltzmann equation using arbitrary order polynomials is presented. The S-model is solved by a discrete ordinate method with velocity space discretized with a truncated Hermite polynomial expansion. Physical space is discretized according to the Conservative Flux Approximation scheme with extension to allow non-uniform grid spacing. This approach, which utilizes Legendre polynomials, allows the spatial representation and ux calculation to be of arbitrary order. High order boundary conditions are implemented. Various results are shown to demonstrate the utility and limitations of the method with comparison to solutions of the Euler and Navier-Stokes equations and from the Direct Simulation Monte Carlo and Uni ed Gas Kinetic schemes. The e ect of both the velocity space discretization and Knudsen number on the convergence properties of the scheme are also investigated.Due to limitations in the geometric adaptability of the new method an implementation of the Uni ed Gas Kinetic Scheme with a variety of enhancements is also presented. These enhancements include internal degree of freedom handling and advanced gas-surface interaction mechanisms including a model of the adsorption and desorption of gas molecules by a surface.The numerical methods developed are used to investigate physical ow phenomena including rare ed e ects such as thermal creep. Pressure gradient inducing thermal creep driven ows in microchannels, commonly referred to as Knudsen pumps, are investigated across a range of rarefaction with particular focus on the e ects of realistic gas coe cients and geometric con guration on performance.A range of geometries are investigated consisting of a previously proposed curved-straight channel and three newly developed channels including a novel two dimensional matrix pump arrangement and classical linear designs. Use of the S-model kinetic equations enables investigation with realistic values of the Prandtl number and viscosity index for argon and nitrogen as well as for Maxwell molecules. The pumping performance and ow structure of each geometry is investigated for a range of channel aspect ratios and Knudsen numbers where the Knudsen numbers are nely spaced between 0.1 and 2.0 to allow approximate performance extrema to be identi ed. The in uence of Prandtl number is found to be signi cant with increased maximum mass ow rates for argon and nitrogen of 5.5-6% when compared to a gas with Maxwellian molecular model. The impact of speci c heat ratio is found to be comparatively minor with a di erence of 0.5% between the argon and nitrogen. The two new channel designs are found to lie between the classical and existing ...

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Parallel computation for Boltzmann equation simulation with Dynamic Discrete Ordinate Method (DDOM)

Cited by 3 publications

References 18 publications

Effects of Easy Hybrid Parallelization with CUDA for OpenMX

Effects of Easy Hybrid Parallelization with CUDA for OpenMX

Effects of Easy Hybrid Parallelization with CUDA for Numerical-Atomic-Orbital Density Functional Theory Calculation

Numerical investigation of gaseous heat and mass transfer: the effect of rarefaction

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