Abstract：The coupled CFD-DEM method has been widely used for multiphase flows where the fluid volume fraction links the continuous medium (fluid) and the discrete medium (particles). This paper presents an improved volume fraction allocation algorithm based on the traditional SKM (statistical kernel method) model with subdividing of the characteristic points. Spatially distributed characteristic points within the region influenced by a particle mark all the CFD cells influenced by the particle so that the particle volume is correctly decomposed into each CFD cell. A traditional grid search algorithm then recognizes the characteristic points. After calibration of the model parameters, the algorithm reduces the truncation error at inner boundaries in parallel computing models. Numerical tests show that the algorithm is effective and efficient when the particle diameter size D and the CFD cell size L are of the same order of magnitude. The model reverts to the traditional unresolved particle model for L >> D and to the resolved particle model for D >> L. The algorithm improves coupled CFD-DEM calculations having a wide range of particle diameters to improve solid-liquid two-phase flow simulations.
刘德天, 傅旭东, 王光谦. CFD-DEM耦合计算中的体积分数算法[J]. 清华大学学报（自然科学版）, 2017, 57(7): 720-727.
LIU Detian, FU Xudong, WANG Guangqian. Volume fraction allocation using characteristic points for coupled CFD-DEM calculations. Journal of Tsinghua University(Science and Technology), 2017, 57(7): 720-727.
Belytschko T, XIAO Shaoping, Schatz G C, et al. Atomistic simulations of nanotube fracture [J]. Physical Review B, 2002, 65: 2354301-2354308.
XIAO Shaoping, Belytschko T. A bridging domain method for coupling continua with molecular dynamics [J]. Computer Methods in Applied Mechanics & Engineering, 2004, 193(17-20): 1645-1669.
PENG Zhengbiao, Doroodchi E, LUO Caimao, et al. Influence of void fraction calculation on fidelity of CFD-DEM simulation of gas-solid bubbling fluidized beds [J]. AIChE Journal, 2014, 60(6): 2000-2018.
ZHU Haiping, YU Aibing. The effects of wall and rolling resistance on the couple stress of granular materials in vertical flow [J]. Physica A: Statistical Mechanics and Its Applications, 2003, 325(3): 347-360.
WU Chunliang, Berrouk A S, Nandakumar K. Three-dimensional discrete particle model for gas-solid fluidized beds on unstructured mesh [J]. Chemical Engineering Journal, 2009, 152(2-3): 514-529.
XIAO Heng, SUN Rui. Algorithms in a robust hybrid CFD-DEM solver for particle-laden flows [J]. Communications in Computational Physics, 2011, 9(2): 297-323.
Babic M. Average balance equations for granular materials [J]. International Journal of Engineering Science, 1997, 35(5): 523-548.
Duggleby A, Camp J L, Doron Y, et al. Massively parallel computational fluid dynamics with large eddy simulation in complex geometries [C]//ASME 2011 International Mechanical Engineering Congress and Exposition. New York, USA: American Society of Mechanical Engineers, 2011: 817-824.
Walker D W, Dongarra J J. MPI: A standard message passing interface [J]. Supercomputer, 1996, 12: 56-68.
Ries A, Brendel L, Wolf D E. Coarse graining strategies at walls [J]. Computational Particle Mechanics, 2014, 1(2): 177-190.
Steinhaus H. Mathematical Snapshots [M]. New York: USA Dover, 1999.
Wells D G. The Penguin Dictionary of Curious and Interesting Numbers [M]. London: Penguin Books, 1986.
SUN Rui, XIAO Heng. Diffusion-based coarse graining in hybrid continuum-discrete solvers: Theoretical formulation and a priori tests [J]. International Journal of Multiphase Flow, 2015, 77: 142-157.
SUN Jin, XIAO Heng, GAO Donghong. Numerical study of segregation using multiscale models [J]. International Journal of Computational Fluid Dynamics, 2009, 23(2): 81-92.
Concha A F. Settling velocities of particulate systems [J]. Kona Powder and Particle Journal, 2009, 27: 18-37.
Cate A T, Nieuwstad C H, Derksen J J, et al. Particle imaging velocimetry experiments and lattice—Boltzmann simulations on a single sphere settling under gravity [J]. Physics of Fluids, 2002, 14(11): 4012-4025.
Peskin C S. Flow patterns around heart valves: A numerical method [J]. Journal of Computational Physics, 1972, 10(2): 252-271.