On DSMC calculations of rarefied gas flows with small number of particles in cells

SIAM Journal on Scientific Computing

Volumn 33, Issue 2, 2011, Pages 677-702

  Stefanov, Stefan K ^a  

^a INSTITUTE OF MECHANICS   (Bulgaria)

Author keywords

Direct simulation monte carlo method; Kinetic theory; Micro gas flows; Rarefied gas flows

Indexed keywords

COMPUTATION THEORY; CYTOLOGY; FLOW OF GASES; GASES; KINETIC THEORY; MESH GENERATION; MONTE CARLO METHODS; NUMERICAL METHODS;

COMPUTATIONAL RESOURCES; DIRECT SIMULATION MONTE CARLO; DIRECT SIMULATION MONTE CARLO CALCULATIONS; DIRECT SIMULATION MONTE CARLO METHOD; MICROGAS FLOW; MONTE CARLO ANALYSIS; PARTICLE IN CELL; RAREFIED GAS FLOW; SUB-CELLS; TIME STEP;

CELLS;

EID: 79957619262     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/090751864     Document Type: Article

References (28)

1. H. BABOVSKY, On a simulation scheme for the Boltzmann equation, Math. Methods Appl. Sci., 8 (1986), pp. 223-233.
2. L. BAKER AND N. HADJICONSTANTINOU, Variance reduction for Monte Carlo solutions of the Boltzmann equation, Phys. Fluids, 17 (2005), 051703.
3. O. M. BELOTSERKOVSKII AND V. E. YANITSKII, The statistical particles-in-cells method for solving rarefied gas dynamics problems, U. S. S. R. Comput. Math. and Math. Phys., 15 (1975), pp. 101-114.
4. G. A. BIRD, Molecular Gas Dynamics, Oxford University Press, Oxford, UK, 1976.
5. G. A. BIRD, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press, Oxford, UK, 1994.
6. A. BOBYLEV AND T. OHWADA, The error of the splitting scheme for solving evolutionary equations, Appl. Math. Lett., 14 (2001), pp. 45-48. (Pubitemid 33616049)
7. C. CERCIGNANI, The Boltzmann Equation and its Applications, Springer, New York, 1988.
8. G. DIMARCO AND L. PARESCHI, Fluid solver independent hybrid methods for multiscale kinetic equations, SIAM J. Sci. Comput., 32 (2010), pp. 603-634.
9. I. DIMOV, I. FARAGO, A. HAVASI, AND Z. ZLATEV, Operator splitting and commutativity analysis in the Danish Eulerian model, Math. Comput. Simulation, 67 (2004), pp. 217-233.
10. J. FAN AND C. SHEN, Statistical simulation of low-speed rarefied gas flows, J. Comput. Phys., 167 (2001), pp. 393-412. (Pubitemid 33652970)
11. M. A. GALLIS, J. R. TORCZYNSKI, D. J. RADER, AND G. A. BIRD, Convergence behavior of a new DSMC algorithm, J. Comput. Phys., 228 (2009), pp. 4532-4548.
12. T. HOMOLLE AND N. HADJICINSTANTINOU, A low-variance deviational simulation Monte Carlo for the Boltzmann equation, J. Comput. Phys., 226 (2007), pp. 2341-2358.
13. M. IVANOV AND S. ROGASINSKY, Theoretical analysis of traditional and modern schemes of the DSMC method, in Proceedings of the 17th Symposium on Rarefied Gas Dynamics, A. Beylich, ed., VCH, New York, 1990, pp. 629-642.
14. K. KOURA, Null-collision technique in the direct simulation Monte Carlo technique, Phys. Fluids, 29 (1986), pp. 3509-3511.
15. S. MIZZI, D. R. EMERSON, S. K. STEFANOV, R. W. BARBER, AND J. M. REESE, Effects of rarefaction on cavity flow in the slip regime, J. Comput. Theor. Nanosci., 4 (2007), pp. 817-822.
16. K. NANBU, Direct simulation scheme derived from the Boltzmann equation, I. Monocomponent gases, J. Phys. Soc. Japan., 49 (1980), pp. 2042-2049.
17. L. PARESCHI AND G. RUSSO, Time relaxed Monte Carlo methods for the Boltzmann equation, SIAM J. Sci. Comput., 23 (2001), pp. 1253-1273.
18. M. A. RIEFFEL, A method for estimating the computational requirements of DSMC simulations, J. Comput. Phys., 149 (1999), pp. 95-113.
19. S. RJASANOW AND W. WAGNER, A stochastic weighted particle method for the Boltzmann equation, J. Comput. Phys., 124 (1996), pp. 243-253. (Pubitemid 126170314)
20. A. A. SHEVYRIN, Y. A. BONDAR, AND M. S. IVANOV, Analysis of repeated collisions in the DSMC method, in Proceedings of the 24th Symposium on Rarefied Gas Dynamics, M. Capitelli, ed., Melville, NY, 2005, pp. 565-570. (Pubitemid 44447081)
21. Y. SONE, Molecular Gas Dynamics: Theory, Techniques, and Applications, Birkhäuser, Boston, 2007.
22. S. STEFANOV, Particle Monte Carlo algorithms with small number of particles in grid cells, in Numerical Methods and Applications, Lecture Notes in Comput. Sci. 6064, I. Dimov, S. Dimova and N. Kilkovska, eds., Springer, Berlin, 2010, pp. 110-117.
23. S. STEFANOV, I. BOYD, AND C. CAI, Monte Carlo analysis of macroscopic fluctuations in a rarefied hypersonic flow around a cylinder, Phys. Fluids, 12 (2000), pp. 1226-1239.
24. S. STEFANOV, V. ROUSSINOV, AND C. CERCIGNANI, Rayleigh-Bénard flow of a rarefied gas and its attractors. III. Three-dimensional computer simulations, Phys. Fluids, 19 (2007), 124101.
25. G. STRANG, On the construction and comparison of difference schemes, SIAM J. Numer. Anal., 5 (1968), pp. 506-517.
26. Q. SUN AND I. BOYD, A direct simulation method for subsonic, microscale gas flows, J. Comput. Phys., 179 (2002), pp. 400-425.
27. W. WAGNER, A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation, J. Statist. Phys., 66 (1992), pp. 1011-1044.
28. V. YANITSKIY, Operator approach to direct simulation Monte Carlo theory in rarefied gas dynamics, in Proceedings of the 17th Symposium on Rarefied Gas Dynamics, A. Beylich, ed., VCH, New York, 1990, pp. 770-777.