×

Automatic mesh refinement and parallel load balancing for Fokker-Planck-DSMC algorithm. (English) Zbl 1392.76066

Summary: Recently, a parallel Fokker-Planck-DSMC algorithm for rarefied gas flow simulation in complex domains at all Knudsen numbers was developed by the authors. Fokker-Planck-DSMC (FP-DSMC) is an augmentation of the classical DSMC algorithm, which mitigates the near-continuum deficiencies in terms of computational cost of pure DSMC. At each time step, based on a local Knudsen number criterion, the discrete DSMC collision operator is dynamically switched to the Fokker-Planck operator, which is based on the integration of continuous stochastic processes in time, and has fixed computational cost per particle, rather than per collision. In this contribution, we present an extension of the previous implementation with automatic local mesh refinement and parallel load-balancing. In particular, we show how the properties of discrete approximations to space-filling curves enable an efficient implementation. Exemplary numerical studies highlight the capabilities of the new code.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
65C05 Monte Carlo methods
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
35Q84 Fokker-Planck equations

Software:

MONACO; CUDA
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bird, G., Molecular gas dynamics and the direct simulation of gas flows, (1994), Oxford University Press
[2] Jenny, P.; Torrilhon, M.; Heinz, S., A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion, J. Comput. Phys., 229, 4, 1077-1098, (2010) · Zbl 1285.76031
[3] Gorji, M. H.; Jenny, P., An efficient particle Fokker-Planck algorithm for rarefied gas flows, J. Comput. Phys., 262, 325-343, (2014) · Zbl 1349.82045
[4] Gorji, M. H.; Jenny, P., Fokker-Planck-DSMC algorithm for simulations of rarefied gas flows, J. Comput. Phys., 287, 110-129, (2015) · Zbl 1351.82074
[5] Küchlin, S.; Jenny, P., Parallel Fokker-Planck-DSMC algorithm for rarefied gas flow simulation in complex domains at all Knudsen numbers, J. Comput. Phys., 328, 258-277, (2017) · Zbl 1406.76072
[6] Gorji, M. H.; Jenny, P., A Fokker-Planck based kinetic model for diatomic rarefied gas flows, Phys. Fluids, 25, 6, (1994), (1994-present)
[7] M.H. Gorji, private communication, 2017.; M.H. Gorji, private communication, 2017.
[8] Gorji, M.; Torrilhon, M.; Jenny, P., Fokker-Planck model for computational studies of monatomic rarefied gas flows, J. Fluid Mech., 680, 574-601, (2011) · Zbl 1241.76342
[9] Bader, M., Space-filling curves - an introduction with applications in scientific computing, Texts in Computational Science and Engineering, vol. 9, (2013), Springer Berlin Heidelberg · Zbl 1283.68012
[10] Aftosmis, M. J.; Berger, M. J.; Murman, S. M., Applications of space-filling curves to Cartesian methods for cfd, (2004), AIAA Paper 2004-1232
[11] Lintermann, A.; Schlimpert, S.; Grimmen, J.; Günther, C.; Meinke, M.; Schröder, W., Massively parallel grid generation on hpc systems, Comput. Methods Appl. Mech. Eng., 277, 131-153, (2014) · Zbl 1423.76366
[12] Schneiders, L.; Grimmen, J. H.; Meinke, M.; Schröder, W., An efficient numerical method for fully-resolved particle simulations on high-performance computers, PAMM, 15, 1, 495-496, (2015)
[13] Green, S., Cuda particles, NVIDIA whitepaper, 2, 3.2, 1, (2008)
[14] Harlacher, D. F.; Klimach, H.; Roller, S.; Siebert, C.; Wolf, F., Dynamic load balancing for unstructured meshes on space-filling curves, (Parallel and Distributed Processing Symposium Workshops PhD Forum (IPDPSW), 2012 IEEE 26th International, (2012)), 1661-1669
[15] Jambunathan, R.; Levin, D. A., A hybrid cpu-gpu parallel octree direct simulation Monte Carlo approach, (AIAA Aviation, American Institute of Aeronautics and Astronautics, (2015))
[16] Jambunathan, R.; Levin, D. A., Grid-free octree approach for modeling heat transfer to complex geometries, J. Thermophys. Heat Transf., 30, 2, 379-393, (2016)
[17] Jambunathan, R.; Levin, D. A., Forest of octree DSMC simulations of flow through porous media, AIP Conf. Proc., 1786, 1, (2016)
[18] Pfeiffer, M.; Gorji, M., Adaptive particle-cell algorithm for Fokker-Planck based rarefied gas flow simulations, Comput. Phys. Commun., (2016) · Zbl 1376.76058
[19] Haverkort, H., How many three-dimensional Hilbert curves are there? · Zbl 1396.28012
[20] Campbell, P. M.; Devine, K. D.; Flaherty, J. E.; Gervasio, L. G.; Teresco, J. D., Dynamic octree load balancing using space-filling curves, (2003), Williams College Department of Computer Science, p. 68
[21] Pinar, A.; Tabak, E. K.; Aykanat, C., One-dimensional partitioning for heterogeneous systems: theory and practice, J. Parallel Distrib. Comput., 68, 11, 1473-1486, (2008) · Zbl 1243.68073
[22] Pinar, A.; Aykanat, C., Fast optimal load balancing algorithms for 1D partitioning, J. Parallel Distrib. Comput., 64, 8, 974-996, (2004) · Zbl 1068.68038
[23] Hoefler, T.; Siebert, C.; Lumsdaine, A., Scalable communication protocols for dynamic sparse data exchange, ACM SIGPLAN Not., 45, 5, 159-168, (2010)
[24] Gropp, W.; Hoefler, T.; Thakur, R.; Lusk, E., Using advanced MPI: modern features of the message-passing interface, (2014), MIT Press
[25] Allègre, J.; Bisch, D.; Lengrand, J., Experimental rarefied density flowfields at hypersonic conditions over 70-degree blunted cone, J. Spacecr. Rockets, 34, 6, 714-718, (1997)
[26] Dietrich, S.; Boyd, I. D., Scalar and parallel optimized implementation of the direct simulation Monte Carlo method, J. Comput. Phys., 126, 2, 328-342, (1996) · Zbl 0856.65002
[27] Gao, D.; Zhang, C.; Schwartzentruber, T., A three-level Cartesian geometry-based implementation of the DSMC method, (Aerospace Sciences Meetings, (2010), American Institute of Aeronautics and Astronautics)
[28] Gao, D.; Zhang, C.; Schwartzentruber, T. E., Particle simulations of planetary probe flows employing automated mesh refinement, J. Spacecr. Rockets, 48, 3, 397-405, (2011)
[29] Allègre, J.; Bisch, D.; Lengrand, J., Experimental rarefied heat transfer at hypersonic conditions over 70-degree blunted cone, J. Spacecr. Rockets, 34, 6, 724-728, (1997)
[30] Hoefler, T.; Traeff, J. L., Sparse collective operations for MPI, (Proceedings of the 2009 IEEE International Symposium on Parallel & Distributed Processing, IPDPS ’09, (2009), IEEE Computer Society Washington, DC, USA), 1-8
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.