Differentially weighted direct simulation Monte Carlo method for particle collision in gas–solid flows

Abrahamson, 1975, Collision rates of small particles in a vigorously turbulent fluid, Chemical Engineering Science, 30, 1371, 10.1016/0009-2509(75)85067-6 Bird, 1976, Vol. 76, 40225 Bird, 1989, Perception of numerical methods in rarefied gas dynamics, Progress in Astronautics and Aeronautics, 117, 211 Bird, 1994 Boyd, 1996, Conservative species weighting scheme for the direct simulation Monte Carlo method, Journal of Thermophysics and Heat Transfer, 10, 579, 10.2514/3.832 Chen, 1999, Direct numerical simulation of droplet collisions in a turbulent channel flow. Part I: collision algorithm, International Journal of Multiphase Flow, 24, 1079, 10.1016/S0301-9322(98)00007-X Chen, 2004, Direct numerical simulation method of inter-particle collision, Chinese Journal of Computational Physics, 21, 421 Cundall, 1979, A discrete numerical model for granular assemblies, Geotechnique, 29, 47, 10.1680/geot.1979.29.1.47 Deutsch, 1991, Large eddy simulation applied to the modelling of particulate transport coefficients in turbulent two-phase flows, 10 Illner, 1987, On simulation methods for the Boltzmann equation, Transport Theory and Statistical Physics, 16, 141, 10.1080/00411458708204655 Ivanov, 1988, Analysis of numerical techniques of the direct simulation Monte Carlo method in the rarefied gas dynamics, Russian Journal of Numerical Analysis and Mathematical Modelling, 3, 453, 10.1515/rnam.1988.3.6.453 Koura, 1986, Null-collision technique in the direct-simulation Monte Carlo method, Physics of Fluids, 29, 3509, 10.1063/1.865826 Lin, 2002, Solution of the population balance equation using constant-number Monte Carlo, Chemical Engineering Science, 57, 2241, 10.1016/S0009-2509(02)00114-8 Lun, 1997, Numerical simulation of dilute turbulent gas–solid flows in horizontal channels, International Journal of Multiphase Flow, 23, 575, 10.1016/S0301-9322(96)00087-0 Nanbu, 1980, Direct simulation scheme derived from the Boltzmann equation. I. Monocomponent gases, Journal of the Physical Society of Japan, 49, 2042, 10.1143/JPSJ.49.2042 Oesterle, 1993, Simulation of particle-to-particle interactions in gas solid flows, International Journal of Multiphase Flow, 19, 199, 10.1016/0301-9322(93)90033-Q Smith, 1998, Constant-number Monte Carlo simulation of population balances, Chemical Engineering Science, 53, 1777, 10.1016/S0009-2509(98)00045-1 Sommerfeld, 2001, Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence, International Journal of Multiphase Flow, 27, 1829, 10.1016/S0301-9322(01)00035-0 Squires, 1990, Particle response and turbulence modification in isotropic turbulence, Physics of Fluids A: Fluid Dynamics, 2, 1191, 10.1063/1.857620 Sundaram, 1996, Numerical considerations in simulating a turbulent suspension of finite-volume particles, Journal of Computational Physics, 124, 337, 10.1006/jcph.1996.0064 Tanaka, 1995, Effects of particle properties on the structure of clusters, ASME-Publications-FED, 228, 297 Tsuji, 1993, Discrete particle simulation of two-dimensional fluidized bed, Powder Technology, 77, 79, 10.1016/0032-5910(93)85010-7 Tsuji, 1998, Cluster patterns in circulating fluidized beds predicted by numerical simulation (discrete particle model versus two-fluid model), Powder Technology, 95, 254, 10.1016/S0032-5910(97)03349-4 Wang, 1998, On the collision rate of small particles in isotropic turbulence. I. Zero-inertia case, Physics of Fluids, 10, 266, 10.1063/1.869565 Wang, 2000, Statistical mechanical description and modelling of turbulent collision of inertial particles, Journal of Fluid Mechanics, 415, 117, 10.1017/S0022112000008661 Wang, 2013, Lattice Boltzmann method for simulations of gas–particle flows over a backward-facing step, Journal of Computational Physics, 239, 57, 10.1016/j.jcp.2012.12.032 Wassen, 2001, Simulation of cluster formation in gas–solid flow induced by particle–particle collisions, International Journal of Multiphase Flow, 27, 437, 10.1016/S0301-9322(00)00028-8 Xu, 2014, Simulation and investigation of periodic deflecting oscillation of gas-solid planar opposed jets, Chemical Engineering and Processing: Process Intensification, 76, 6, 10.1016/j.cep.2013.11.009 Zhao, 2014, Dependence of steady-state compositional mixing degree on feeding conditions in two-component aggregation, Industrial & Engineering Chemistry Research, 53, 6047, 10.1021/ie500316g Zhao, 2009, Reducing statistical noise and extending the size spectrum by applying weighted simulation particles in Monte Carlo simulation of coagulation, Aerosol Science and Technology, 43, 781, 10.1080/02786820902939708 Zhao, 2010, A differentially weighted Monte Carlo method for two-component coagulation, Journal of Computational Physics, 229, 6931, 10.1016/j.jcp.2010.05.031 Zhao, 2011, Monte Carlo simulation for aggregative mixing of nanoparticles in two-component systems, Industrial & Engineering Chemistry Research, 50, 10652, 10.1021/ie200780q Zhao, 2009, A new event-driven constant-volume method for solution of the time evolution of particle size distribution, Journal of Computational Physics, 228, 1412, 10.1016/j.jcp.2008.10.033 Zhao, 2009, Correcting the multi-Monte Carlo method for particle coagulation, Powder Technology, 193, 120, 10.1016/j.powtec.2009.01.019 Zhao, 2013, A population balance – Monte Carlo method for particle coagulation in spatially inhomogeneous systems, Computers & Fluids, 71, 196, 10.1016/j.compfluid.2012.09.025 Zhou, 1993