×

The implementation of subsonic boundary conditions for the direct simulation Monte Carlo method in dsmcFoam. (English) Zbl 1390.65006

Summary: New treatments of the subsonic constant flow rate boundary and porous outlet boundary used for the direct simulation Monte Carlo (DSMC) method are proposed. For the constant flow rate boundary, the total number of molecules inserted is calculated using the number of molecules that flow out of the boundary at previous time step, and the molecules inserted over the boundary are distributed according to the local mean flow velocity and number density. For the porous outlet, it is used to simulate the vacuum pump, and the deleting probability is calculated using the number of molecules that impinge on the boundary, the local pressure and the pump speed. Except for the constant flow inlet and porous outlet, the pressure inlet/outlet and the outgassing wall boundaries are implemented in dsmcFoam and verified. The results of different treatments of the boundary are compared with each other, it shows that the new treatment of the constant flow rate boundary can achieve a more accurate flow rate, and the non-uniform distribution of the inserted molecules can decrease the averaging effect at the inlet; the porous outlet can achieve the desired pressure at the outlet when just giving the pump speed, but there is an averaging effect compared with the pressure outlet due to the uniform deleting probability. The results are also compared with that of DS2V when the boundary conditions are available, it shows that the constant pressure boundary can achieve a more accurate pressure in dsmcFoam than in DS2V, and the results of the outgassing wall are almost the same with both solvers.

MSC:

65C05 Monte Carlo methods
76M35 Stochastic analysis applied to problems in fluid mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
Full Text: DOI

References:

[1] Bird, GA, Molecular gas dynamics and the direct simulation of gas flows, (1998), Clarendon Press
[2] Gatsonis, NA; Chamberlin, RE; Averkin, SN, An unstructured direct simulation Monte Carlo methodology with kinetic-moment inflow and outflow boundary conditions, J Comput Phys, 233, 148-174, (2013) · Zbl 1286.65004
[3] Lei, M; Li, X; Wang, J; Chen, B, The angular distribution at the outlet of a capillary in a wide range of rarefaction, Vacuum, 132, 40-46, (2016)
[4] Nance, RPR; Hash, DDB; Hassan, HAH; Nance, R. P.; Hash, D. B.; Hassan, HA, Role of boundary conditions in Monte Carlo simulation of microelectromechanical systems, J Thermophys Heat Transf, 12, 447-449, (1998)
[5] Chen, G; Boyd, ID, Monte Carlo analysis of a hyperthermal silicon deposition process, J Vac Sci Technol A, 16, 689-699, (1998)
[6] Hash, D; Meyyappan, M, A direct simulation Monte Carlo study of flow considerations in plasma reactor development for 300 mm processing, J Electrochem Soc, 144, 3999-4004, (1997)
[7] Deng, H; Li, Z; Levin, D; Gochberg, L; Levin, DA; Wysong, IJ, Investigation of the DSMC approach for ion/neutral species in modeling low pressure plasma reactor, AIP Conf Proc-American Inst Phys, 1333, 1033, (2011)
[8] Liou, WW; Fang, YC, Implicit boundary conditions for direct simulation Monte Carlo method in MEMS flow predictions, Comput Model Eng Sci, 1, 119-128, (2000)
[9] Cai, C; Boyd, ID; Fan, J; Candler G, V, Direct simulation methods for low-speed microchannel flows, J Thermophys Heat Transf, 14, 368-378, (2000)
[10] Wu, J-S; Tseng, K-C, Analysis of micro-scale gas flows with pressure boundaries using direct simulation Monte Carlo method, Comput Fluids, 30, 711-735, (2001) · Zbl 1167.76356
[11] Sun, Q; Boyd, ID, A direct simulation method for subsonic, microscale gas flows, J Comput Phys, 179, 400-425, (2002) · Zbl 1130.76416
[12] Wang, M; Li, Z, Simulations for gas flows in microgeometries using the direct simulation Monte Carlo method, Int J Heat Fluid Flow, 25, 975-985, (2004)
[13] Farbar, E; Boyd, ID, Subsonic flow boundary conditions for the direct simulation Monte Carlo method, Comput Fluids, 102, 99-110, (2014) · Zbl 1391.76677
[14] Ye, JJ; Yang, J; Zheng, JY; Li, WZ; He, SZ; Ma, YB, New treatment of pressure boundary conditions for DSMC method in micro-channel flow simulations, Toin Law Rev, 22, 85-93, (2007)
[15] Wu, JS; Lee, WS; Lee, F; Wong, SC, Pressure boundary treatment in internal gas flows at subsonic speed using the DSMC method, Rarefied Gas Dyn, 585, 408-416, (2001)
[16] Bird, GA., The DS2V/3 V program suite for DSMC calculations, AIP Conf Proc, 762, 541-546, (2005)
[17] Scanlon, TJ; Roohi, E; White, C; Darbandi, M; Reese, JM, An open source, parallel DSMC code for rarefied gas flows in arbitrary geometries, Comput Fluids, 39, 2078-2089, (2010) · Zbl 1245.76127
[18] Borg M. MicroNanoFlows/OpenFOAM-2.4.0-MNF. https://github.com/MicroNanoFlows/OpenFOAM-240-MNF n.d; Borg M. MicroNanoFlows/OpenFOAM-2.4.0-MNF. https://github.com/MicroNanoFlows/OpenFOAM-240-MNF n.d
[19] Sharipov, F; Seleznev, V, Data on internal rarefied gas flows, J Phys Chem Ref Data, 27, 657, (1998)
[20] Roohi, E; Stefanov, S, Collision partner selection schemes in DSMC: from micro/nano flows to hypersonic flows, Phys Rep, 656, 1-38, (2016)
[21] Bird GA. The DSMC method. Self-published through CreateSpace, an Amazon company; 2013.; Bird GA. The DSMC method. Self-published through CreateSpace, an Amazon company; 2013.
[22] 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
[23] Arkilic, EB; Schmidt, MA; Breuer, KS, Gaseous slip flow in long microchannels, J Microelectromech Syst, 6, 167-178, (1997)
[24] Dongari, N; Agrawal, A; Agrawal, A, Analytical solution of gaseous slip flow in long microchannels, Int J Heat Mass Transf, 50, 3411-3421, (2007) · Zbl 1151.76417
[25] Fedosov, DA; Rogasinsky, SV; Zeifman, MI; Ivanov, MS; Alexeenko, AA; Levin, DA, Analysis of numerical errors in the DSMC method, AIP Conf Proc, 762, 589-594, (2005)
[26] Hadjiconstantinou, NG; Garcia, AL; Bazant, MZ; He, G, Statistical error in particle simulations of hydrodynamic phenomena, J Comput Phys, 187, 274-297, (2003) · Zbl 1047.76578
[27] Plotnikov, MY; Shkarupa, EV, Theoretical and numerical analysis of approaches to evaluation of statistical error of the DSMC method, Comput Fluids, 105, 251-261, (2014) · Zbl 1391.76683
[28] White, C; Borg, MK; Scanlon, TJ; Reese, JM, A DSMC investigation of gas flows in micro-channels with bends, Comput Fluids, 71, 261-271, (2013) · Zbl 1365.76284
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.