Simulation of pure sedimentation of raindrops using quadrature method of moments

Beheng, 1986, A general formulation of collection rates of cloud and raindrops using the kinetic equation and comparison with parameterizations, Beitr. Phys. Atmos., 59, 66 Bott, 1997, A numerical model of the cloud-topped planetary boundary layer: impact of aerosol particles on the radiative forcing of stratiform clouds, Q. J. R. Meteorol. Soc., 123, 631, 10.1002/qj.49712353906 Carneiro, 2008, Implementation of a Moments Model in OpenFOAM for polydispersed multiphase flows Carneiro, 2009, Numerical simulation of droplet dispersion and evaporation with a moments-based CFD model Drumm, 2009, Coupling of CFD with DPBM for an RDC extractor, Chem. Eng. Sci., 64, 721, 10.1016/j.ces.2008.05.041 Enukashvili, 1964, On the solution of the kinetic coagulation equation, Akad. Nauk. SSSR Izv. Geofiz. Ser., 10, 944 Feingold, 1988, Evolution of raindrop spectra. Part I: solution to the stochastic collection/breakup equation using the method of moments, J. Atmos. Sci., 45, 3387, 10.1175/1520-0469(1988)045<3387:EORSPI>2.0.CO;2 Hall, 1980, A detailed microphysical model within a two-dimensional dynamic framework: model description and preliminary results, J. Atmos. Sci., 37, 2486, 10.1175/1520-0469(1980)037<2486:ADMMWA>2.0.CO;2 Hu, 1995, Evolution of raindrop size distribution by coalescence, breakup and evaporation: Theory and Observations, J. Atmos. Sci., 52, 1761, 10.1175/1520-0469(1995)052<1761:EORSDB>2.0.CO;2 Kessler, 1969 Khain, 2000, Notes on the state-of-the-art numerical modeling of cloud microphysics, Atmos. Res., 55, 159, 10.1016/S0169-8095(00)00064-8 Kogan, 1991, The simulation of a convective cloud in a 3-D model with explicit microphysics. Part 1: model description and sensitivity experiments, J. Atmos. Sci., 48, 1160, 10.1175/1520-0469(1991)048<1160:TSOACC>2.0.CO;2 Kumar, 1996, On the solution of population balance equations by discretization—I. A fixed pivot technique, Chem. Eng. Sci., 51, 1311, 10.1016/0009-2509(96)88489-2 Laurent, 2010, Quadrature method of moments for modeling multi-component spray vaporization, Int. J. Multiphase Flow, 36, 51, 10.1016/j.ijmultiphaseflow.2009.08.005 Lin, 1983, Bulk parameterization of the snow field in a cloud model, J. Clim. Appl. Meteorol., 22, 1065, 10.1175/1520-0450(1983)022<1065:BPOTSF>2.0.CO;2 Lüpkes, 1989, A parameterization scheme for simulating collision-coalescence of water drops, Beitr. Phys. Atmos., 62, 289 Marchisio, 2003, Quadrature method of moments for aggregation–breakage processes, J. Colloid Interface Sci., 258, 322, 10.1016/S0021-9797(02)00054-1 Marshall, 1948, The distribution of raindrops with size, J. Meteorol., 5, 165, 10.1175/1520-0469(1948)005<0165:TDORWS>2.0.CO;2 McFarquhar, 1991, The raindrop mean free path and collision rate dependence on rainrate for three-peak equilibrium and Marshall–Palmer distributions, J. Atmos. Sci., 48, 1999, 10.1175/1520-0469(1991)048<1999:TRMFPA>2.0.CO;2 McGraw, 1997, Description of aerosol dynamics by the quadrature method of moments, Aerosol Sci. Technol., 27, 255, 10.1080/02786829708965471 Meyers, 1997, New RAMS cloud microphysics parameterization: Part II. The two-moment scheme, Atmos. Res., 45, 3, 10.1016/S0169-8095(97)00018-5 Milbrandt, 2005, A multimoment bulk microphysics parameterization. Part I: analysis of the role of the spectral shape parameter, J. Atmos. Sci., 62, 3051, 10.1175/JAS3534.1 Milbrandt, 2005, A multimoment bulk microphysics parameterization. Part II: a proposed three-moment closure and scheme description, J. Atmos. Sci., 62, 3065, 10.1175/JAS3535.1 Prat, 2007, A robust numerical solution of the stochastic collection–breakup equation for warm rain, J. Appl. Meteorol. Climatol., 46, 1480, 10.1175/JAM2544.1 Seifert, 2000, An improved parameterization for simulating autoconversion, accretion and selfcollection based on a double-moment scheme, 493 Seifert, 2006, A two-moment cloud microphysics parameterization for mixed-phase clouds. Part 1: model description, Meteorol. Atmos. Phys., 92, 45, 10.1007/s00703-005-0112-4 Tzivion, 1987, An efficient numerical solution to the stochastic collection equation, J. Atmos. Sci., 44, 3139, 10.1175/1520-0469(1987)044<3139:AENSTT>2.0.CO;2 Wacker, 2009, On the selection of prognostic moments in parametrization schemes for drop sedimentation, Tellus, 61A, 498, 10.1111/j.1600-0870.2009.00405.x Wacker, 2001, Evolution of rain water profiles resulting from pure sedimentation: spectral vs. parameterized description, Atmos. Res., 58, 19, 10.1016/S0169-8095(01)00081-3 Walko, 1995, New RAMS cloud microphysics parameterization. Part I: the single-moment scheme, Atmos. Res., 38, 29, 10.1016/0169-8095(94)00087-T