×

Development of parallel direct simulation Monte Carlo method using a cut-cell Cartesian grid on a single graphics processor. (English) Zbl 1391.76680

Summary: This study developed a parallel two-dimensional direct simulation Monte Carlo (DSMC) method using a cut-cell Cartesian grid for treating geometrically complex objects using a single graphics processing unit (GPU). Transient adaptive sub-cell (TAS) and variable time-step (VTS) approaches were implemented to reduce computation time without a loss in accuracy. The proposed method was validated using two benchmarks: 2D hypersonic flow of nitrogen over a ramp and 2D hypersonic flow of argon around a cylinder using various free-stream Knudsen numbers. We also detailed the influence of TAS and VTS on computational accuracy and efficiency. Our results demonstrate the efficacy of using TAS in combination with VTS in reducing computation times by more than 10\(\times\). Compared to the throughput of a single core Intel CPU, the proposed approach using a single GPU enables a 13–35\(\times\) increase in speed, which varies according to the size of the problem and type of GPU used in the simulation. Finally, the transition from regular reflection to Mach reflection for supersonic flow through a channel was simulated to demonstrate the efficacy of the proposed approach in reproducing flow fields in challenging problems.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76K05 Hypersonic flows
65C05 Monte Carlo methods
76M28 Particle methods and lattice-gas methods

Software:

CUDA; MONACO
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bird, G. A., Molecular gas dynamics and the direct simulation of gas flows, (1994), Oxford Univ Press
[2] Nanbu, K., Direct simulation scheme derived from the Boltzmann equation I: mono component gases, J Phys Soc Jpn, 49, 5, 2042-2049, (1980)
[3] Wagner, W., A convergence proof for bird’s direct simulation Monte Carlo method for the Boltzmann equation, J Stat Phys, 66, 1011-1044, (1992) · Zbl 0899.76312
[4] Dietrich, S.; Boyd, I. D., Scalar and parallel optimized implementation of the direct simulation Monte Carlo method, J Comput Phys, 126, 328-342, (1996) · Zbl 0856.65002
[5] Ivanov, M.; Markelov, G.; Taylor, S.; Watts, J., Parallel DSMC strategies for 3D computations, Proc Parallel CFD, 96, 485-492, (1997)
[6] LeBeau, G. J., A parallel implementation of the direct simulation Monte Carlo method, Comput Methods Appl Mech Eng, 174, 319-337, (1999) · Zbl 0961.76076
[7] Su, C.-C.; Smith, M. R.; Wu, J.-S.; Hsieh, C.-W.; Tseng, K.-C.; Kuo, F.-A., Large-scale simulations on multiple graphics processing units (GPUs) for the direct simulation Monte Carlo method, J Comput Phys, 231, 7932-7958, (2012)
[8] Su C-C, Hsieh C-W, Smith MR, Jermy MC, Wu J-S. Parallel direct simulation Monte Carlo computation using CUDA on GPUs. In: Proceedings of the 27th international symposium on rarefied gas dynamics, Pacific Grove, California, USA; July 2010.
[9] Gladkov, D.; Tapia, J. J.; Alberts, S.; D’Souza, R. M., Graphics processing unit based direct simulation Monte Carlo, Simulation, 88, 6, 680-693, (2012)
[10] Wu, J.-S.; Lian, Y.-Y., Parallel three-dimensional direct simulation Monte Carlo method and its applications, Comput Fluids, 32, 1133-1160, (2003) · Zbl 1098.76599
[11] Boyd, I. D., Vectorization of a Monte Carlo simulation scheme for nonequilibrium gas dynamics, J Comput Phys, 96, 2, 411-427, (1991) · Zbl 0726.76076
[12] Bird GA. Sophisticated versus simple DSMC. In: Proceedings of the 25th international symposium on rarefied gas dynamics (RGD25); 2006.
[13] Bird GA. The DS2V/3V program suite for DSMC calculations. In: Capitelli M, editor. Rarefied gas dynamics: proceedings of the 24th international symposium on rarefied gas dynamics, AIP conference proceedings, vol. 762. Melville, NY; 2005. p. 541-6.
[14] Su, C.-C.; Tseng, K.-C.; Cave, H. M.; Wu, J.-S.; Lian, Y.-Y.; Kuo, T.-C., Implementation of a transient adaptive sub-cell module for the parallel-DSMC code using unstructured grids, Comput Fluids, 39, 1136-1145, (2010) · Zbl 1242.76289
[15] Kannenberg, K. C.; Boyd, I. D., Strategies for efficient particle resolution in the direct simulation Monte Carlo method, J Comput Phys, 157, 727-745, (2000) · Zbl 1051.76051
[16] Wu, J.-S.; Tseng, K.-C.; Wu, F.-Y., Parallel three-dimensional DSMC method using mesh refinement and variable time-step scheme, J Comput Phys Commun, 162, 166-187, (2004) · Zbl 1196.65027
[17] NVIDIA corp. NVIDIA compute unified device architecture programming guide version 1.0; 2007.
[18] NVIDIA crop. NVIDIA CUDA C programming guide version 4.0; 2011.
[19] Eric, H., Point in polygon strategies, (Heckbert, Paul., Graphics gems IV, (1994), Academic Press), 24-46 · Zbl 0821.68118
[20] Zhang, C.-L.; Schwartzentruber, T. E., Robust cut-cell algorithms for DSMC implementations employing multi-level Cartesian grids, Comput Fluids, 69, 122-135, (2012) · Zbl 1365.76268
[21] Gallis, M. A.; Torczynski, J. R.; Rader, D. J.; Bird, G. A., Accuracy and convergence of a new DSMC algorithm, AIAA J, 2008-3913, (2008)
[22] Moss JN, Rault DF, Price JM. Direct Monte Carlo simulations of hypersonic viscous interactions including separation. In: Shizgal BD, Weaver DP, editors. Rarefied gas dynamics: space science and engineering; 1993. p. 209-20.
[23] Wu, J.-S.; Tseng, K.-C., Parallel particle simulation of the near-continuum hypersonic flows over compression ramps, ASME J Fluids Eng, 125, 1, 181-188, (2003)
[24] Moss JN, Price JM, Chun CH. Hypersonic rarefied flow about a compression corner—DSMC simulation and experiment. In: 26th thermophysics conference, AIAA paper, no 91-1313; 1991.
[25] Lofthouse, A. J.; Boyd, I. D.; Wright, J. M., Effects of continuum breakdown on hypersonic aerothermodynamics, Phys Fluids, 19, 027105, (2007) · Zbl 1146.76470
[26] Ivanov, M. S.; Markelov, G. N.; Kudryavtsev, A. N.; Gimelshein, S. F., Numerical analysis of shock wave reflection transition in steady flows, AIAA J, 36, 11, 2079-2086, (1998)
[27] Ivanov, M. S.; Kudryavtsev, A. N.; Nikiforov, S. B.; Khotyanovsky, D. V.; Pavlov, A. A., Experiments on shock wave reflection transition and hysteresis in low-noise wind tunnel, Phys Fluids, 15, 6, 1807-1810, (2003) · Zbl 1186.76252
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.