References
- Baines , W.D. and Hopfinger , E.J. 1984 . Thermals with Large Density Difference . Atmos. Environ. , 18 ( 6 ) : 1051 – 1057 .
- Bugliarello , G. and Jackson , E.D. 1964 . Random Walk Study of Convective Diffusion . ASCE J. Engng. Mech. Div. , 94
- Bühler , J. and Papantoniou , D.A. 1991 . “ Swarms of Coarse Particles Falling Through a Fluid ” . In Environmental Hydraulics , Edited by: Lee and Chung . 135 – 140 . Rotterdam : Balkema .
- Bühler , J. and Papantoniou , D.A. 2001 . On the Motion of Suspension Thermal and Particle Swarms . J. Hydraul. Res., IAHR , 39 ( 6 ) : 643 – 654 .
- Chiu , C.-L. 1967 . Stochastic Models of Motion of Solid Particles . Proc. ASCE , HY5 : 203 – 218 .
- Crowe , C.T. , Sharma , M.P. and Stock , D.E. 1977 . The Particle-Source in Cell (PSI-CELL) Model for Gas-Droplet Flows . ASMEJ. Fluids Engng , 99 : 325
- Elghobashi , S. and Abou-Arab , T.W. 1983 . A Two- Equation Turbulence Model for Two-Phase Flows . Phys. Fluids , 25 : 931 – 938 .
- Kramer , T.J. and Depew , C.A. 1972 . Ananlysis of Mean Flow Characterisitcs of Gas-Solid Suspensions . J. Basic Engng. Trans. ASME , 94D : 731
- Li , C.W. 1990 . Advection Simulation by Minimax- Characteristics Method . J. Hydraul. Engng. ASCE , 116 ( 9 ) : 1138 – 1144 .
- Li , C. W. 1997 . Convection of Particle Thermals . J. Hydraul. Res., IAHR , 35 ( 3 ) : 363 – 376 .
- Maier-Reimer , E. and Sundermann , J. 1982 . On Tracer Methods in Computational Hydrodynamics . Engng Appl. Comput. Hydraul. , I : 198 – 217 .
- Nakatsuji , K. , Tamai , M. and Murota , A. Int. Conf. on Phys. Modelling of Transport and Dispersion . Dynamic Behaviors of Sand Clouds in Water , MIT Boston, 8C.1 .
- Naot , D. , Nezu , I. and Nakagawa , H. 1996 . Hydro- dynamic Behavior of Partly Vegetated Open Channels . J. Hydraul. Engng., ASCE , 122 ( 11 ) : 625 – 633 .
- Noh , Y. and Fernando , HJ.S. 1993 . The Transition in the Sedimentation Pattern of a Particle Cloud . Phys. Fluids A , 5 : 3049 – 3055 .
- Richards , J.M. 1963 . Experiments on the Motions of Isolated Cylindrical Thermals Through Unstratified Surroundings . Int. J. Air Water Pollut. , 7 : 17 – 34 .
- Scorer , R.S. 1957 . Experiments on Convection of Isolated Masses of Buoyant Fluid . J. Fluid Mech. , 2 : 583 – 594 .
- Snider , D.M. 2001 . An Incompressible Three- dimensional Multiphase Particle-in-Cell Model for Dense Particle Flows . J. Comput. Phys. , 170 : 523 – 549 .
- Soo , S.L. 1967 . Fluid Dynamics of Multiphase Systems , Waltham : Blasisdell .
- Yanenko , N.N. 1971 . The Method of Fractional Steps , New York : Springer .
- Yokomine , T. , Shimizu , A. , Kawamura , H. and Hasegawa , S. 1994 . Realistic Modeling of Turbulence Modulations in k-ϵ Equations for Gas-Solid Flows . Numer. Methods Multiphase Flows, ASME , 185 : 301 – 306 . FED-