A parallel implementation of the direct simulation Monte Carlo method. (English) Zbl 0961.76076

Summary: The underlying assumptions used to formulate the Navier-Stokes equations preclude their use for the analysis of rarefied gas dynamic environments. Alternatively, the direct simulation Monte Carlo technique (DSMC) can be used to numerically investigate such flows. In this methodology, molecules are tracked through representative collisions and boundary interactions. This microscopic view on the flow allows the inclusion of internal energy modes and chemical reactions in a direct and physical manner. This well-established methodology is combined with innovative strategies to improve the performance and overall capabilities of the technique. Beyond basic procedural enhancements, a parallel implementation of the DSMC method is developed using the master/slave programming model. This new tool is applied to several example problems. These are used to compare the performance of the parallel code to a comparable scalar implementation and to investigate the dynamic load balancing capabilities and the overall scalability of the parallel software. High parallel performance is demonstrated using up to 512 processors on a Cray T3E parallel supercomputer.


76M35 Stochastic analysis applied to problems in fluid mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
65Y05 Parallel numerical computation


Full Text: DOI


[1] Vincenti, W. G.; Kruger, C. H., Introduction to Physical Gas Dynamics (1965), Wiley
[2] Nance, R. P., Monte Carlo simulation of three-dimensional hypersonic flows on parallel architectures, (Masters Thesis (1995), North Carolina State University: North Carolina State University New York)
[3] Plimpton, S.; Bartel, T., Parallel Particle Simulations of Low-Density Fluid Flows, U.S. Department of Energy Report No. DE94-007858 (1993)
[4] Bird, G. A., Molecular Gas Dynamics and the Direct Simulation of Gas Flows (1994), Clarendon Press · Zbl 0709.76511
[5] Nambu, K., Theoretical basis of the direct simulation Monte Carlo method, J. Phys. Soc. Jpn (1982)
[6] Lumpkin, F. E., Numerical Methods in Rarefied Gas Dynamics, (Class Notes Mech, 604 (1994), Rice University: Rice University Oxford)
[7] Garcia, A. L.; Alexander, F. J.; Alder, B. J., A consistent Boltzmann algorithm, Phys. Rev. Lett., 74, 26, 5212-5215 (1995)
[8] Dietrich, S.; Boyd, I. D., Parallel implementation on the IBM SP-2 of the direct simulation Monte Carlo method, AIAA Paper No. 95-2029 (1995)
[9] Hedahl, M. O.; Wilmoth, R. G., Comparisons of the Maxwell and CLL gas/surface interaction models using DSMC, NASA Technical Memorandum 110205 (1995)
[10] Bird, G. A., Perception of numerical methods in rarefied gasdynamics, (Proc. 16th Int. Symp. on Rarefied Gas Dynamics (1989), AIAA), 221
[11] Baganoff, D.; McDonald, J. D., A collision selection rule for a particle simulation method suited to vector computers, Phys. Fluids A., 2, 1248-1259 (1990)
[12] Borgnakke, C.; Larsen, P. S., Statistical collision model for Monte Carlo simulation of polyatomic gas mixture, J. Comput. Phys., 18, 4, 405-420 (1975), 4
[13] Bird, G. A., Grids for DSMC computation of two and three-dimensional flows, (Int. Symp. on Computational Fluid Dynamics, 3rd. Int. Symp. on Computational Fluid Dynamics, 3rd, Nagoya, Japan (1989)), 507-512
[14] McDonald, J. D., A computationally efficient particle simulation method suited to vector computer architectures, (Ph.D. Thesis (1989), Stanford University: Stanford University Washington)
[15] Bird, G. A., Application of the direct simulation Monte Carlo method to the full shuttle geometry, AIAA Paper No. 90-1692 (1990)
[16] Thompson, J. F., National grid project, Comput. Syst. Engrg., 3, 1-4 (1992)
[17] Pirzadeh, S., Structured background grids for generation of unstructured grids by advancing-front method, AIAA J., 31, 2, 257-265 (1993)
[18] Melton, J. E.; Berger, M. J.; Aftosmis, M. J.; Wong, M. D., Development and application of a 3D Cartesian grid Euler method, Ssurface modeling, grid generation, and related issues in computational fluid dynamic (CFD) solutions. Ssurface modeling, grid generation, and related issues in computational fluid dynamic (CFD) solutions, NASA CP-3291, 225-250 (1995)
[19] Pearce, D. G.; Stanley, S. A.; Martin, F. W.; Gomez, R. J.; LeBeau, G. J.; Buning, P. G.; Chan, W. M.; Chiu, I.; Wulf, A.; Akdag, V., Development of a large scale chimera grid system for the space shuttle launch vehicle, AIAA Paper No. 93-0533 (1993)
[20] Wilmoth, R. G.; LeBeau, G. J.; Carlson, A. B., DSMC grid methodologies for computing low-density, hypersonic flows about reusable launch vehicles, AIAA Paper No. 96-1812 (1996)
[21] Moss, J. N.; LeBeau, G. J.; Blanchard, R. C.; Price, J. M., Rarefaction effects on Galileo probe aerodynamics, (20th Int. Symp. Rarefied Gas Dynamics. 20th Int. Symp. Rarefied Gas Dynamics, Beijing, China (1996))
[22] Blanchard, R. C.; Wilmoth, R. G.; LeBeau, G. J., Rarefied-flow transition regime orbiter aerodynamic acceleration flight measurements, J. Spacecraft Rockets, 34, 1, 8-15 (1997)
[23] Lumpkin, F. E., Rarefied Cylinder Wake, Houston High Speed Flow Database (1997)
[24] Lumpkin, F. E., Development and evaluation of continuum models for translational-rotational nonequilibrium, (Ph.D. Thesis (1990), Stanford University)
[25] Bird, G. A., (The G2/A3 program system users manual (1992), G.A.B. Consulting Pty Ltd)
[26] Baganoff, D., Vectorization of a particle code used in the simulation of rarefied hypersonic flow, Comput. Syst. Engrg., 1, 2-4 (1990)
[27] Prisco, G., Optimization of direct simulation Monte Carlo (DSMC) codes for vector processing, J. Comput. Phys., 94, 454-466 (1991) · Zbl 0717.76093
[28] Boyd, I. D., Vectorization of a Monte Carlo scheme for nonequilibrium gas dynamics, J. Comput. Phys., 96, 411-427 (1991) · Zbl 0726.76076
[29] McDonald, J. D., Particle simulation in a multiprocessor environment, AIAA Paper No. 91-1366 (1991)
[30] Dagum, L., Three dimensional direct particle simulation on the connection machine, AIAA Paper No. 91-1365 (1991)
[31] Wong, B. C.; Long, L. N., Direct simulation Monte Carlo (DSMC) on the connection machine, AIAA Paper No. 92-0564 (1992)
[32] Wilmoth, R. G., Direct simulation Monte Carlo analysis on parallel processors, AIAA Paper No. 89-1666 (1989)
[33] Wilmoth, R. G.; Carlson, A. B., DSMC analysis in a heterogeneous parallel computing environment, AIAA Paper No. 92-2861 (1992)
[34] Fallavollita, M. A.; McDonald, J. D.; Baganoff, D., Parallel implementation of a particle simulation for modeling rarefied gas dynamic flow, Comput. Syst. Engrg, 3, 1-4, 283-289 (1992)
[35] Ivanov, M.; Markelov, G.; Taylor, S.; Watts, J., Parallel DSMC strategies for 3D computations, (Proceedings of Parallel CFD 96 (1996)), 485-492
[36] Robinson, C. D.; Harvey, J. K., The development of an efficient direct simulation Monte Carlo computation scheme for gas flows in a parallel environment, (Proc. 4th Inter. Parallel Computing Workshop. Proc. 4th Inter. Parallel Computing Workshop, London (1995)), 33-42
[37] (Message Passing Interface Forum MPI: A Message-Passing Interface Standard. Message Passing Interface Forum MPI: A Message-Passing Interface Standard, Computer Science Dept. Technical Report CS-94-230 (1994), University of Tennessee: University of Tennessee Killara N.S.W. Australia) · Zbl 0825.68198
[38] Geist, A.; Beguelin, A.; Dongarra, J.; Jiang, W.; Manchek, R.; Sunderam, V., (PVM 3 Users Guide and Reference Manual (1993), Oak Ridge National Laboratory ORNL/TM-12187)
[39] Bartel, T.; Plimpton, S., DSMC Simulations of low-density fluid flow on MIMD supercomputers, Comput. Syst. Engrg., 3, 1-4, 333-336 (1992)
[40] Watts, J.; Rieffel, M.; Taylor, S., Practical Dynamic Load Balancing for Irregular Problems, (Parallel Algorithms for Irregularly Structured Problems: IRREGULAR 96 Proceedings (1996), Springer-Verlag LNCS), 299-306, 1117
[41] Nance, R. P.; Wilmoth, R. G.; Moon, B.; Hassan, H. A.; Saltz, J., Parallel DSMC solution of three-dimensional flow over a finite flat plate, AIAA Paper No. 94-0219 (1994)
[42] GSFC Site Specific Information (1997)
[43] Cray Research Inc., The Cray T3E Series (1997)
[44] International space station crew return vehicle performance requirements, NASA Space Station Program Document 50306 (1997)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.