Numerical Solution to Drop Coalescence/Breakup with a Volume-Conserving, Positive-Definite, and Unconditionally Stable Scheme

This paper discusses a new volumeand volume concentration–conserving, positive-definite, unconditionally stable iterative numerical scheme for solving temporary cloud/raindrop coalescence followed by breakup and the coupling of the scheme with an existing noniterative, volumeand volume concentration– conserving collision/coalescence (coagulation) scheme. The breakup scheme alone compares nearly exactly with a constant-kernel analytical solution at a 300-s time step. The combined coagulation/breakup schemes are stable and conservative, regardless of the time step and number of size bins, and convergent with higher temporal and size resolution. The schemes were designed with these characteristics in mind for use in longterm global or regional simulations. The use of 30 geometrically spaced size bins and a time step of 60 s provides a good compromise between obtaining sufficient accuracy (relative to a much higher-resolution result) and speed, although solutions with a 600-s time step and 30 bins are stable and conservative and take one-eighth the computer time. The combined coagulation/breakup schemes were implemented into the nested Gas, Aerosol, Transport, Radiation, General Circulation, Mesoscale, and Ocean Model (GATORGCMOM), a global–urban climate–weather–air pollution model. Coagulation was solved over liquid, ice, and graupel distributions and breakup simultaneously over the liquid distribution. Each distribution included 30 size bins and 16 chemical components per bin. Timing tests demonstrate the feasibility of the scheme in long-term global simulations.