A New Family of Methods for Efficiently Calculating Collisional Processes in Bin Models

A new set of methods has been developed for numerically solving collisional equations such as the kinetic collection equation, and evaluated for drop collision-coalescence in a box model. The drop size distribution is approximately reconstructed from the prognostic moments of a bin model as a linear combination of basis functions. Using the given basis, the calculation of collisional process rates is split into two pieces: the calculation of a collision tensor (performed “offline” using numerical quadrature) and the application of that tensor (performed “online”). The online calculations are written as a set of matrix multiplications, so efficient implementation on GPUs is straightforward. The error of the scheme depends almost solely on (1) the reconstruction method used for the given prognostic moments and basis functions, and (2) the time integration method that uses the process rates to evolve the model state. This approach is very flexible, accommodating single- and multi-moment schemes, non-uniform bin widths, stability over long time steps, conservative transfer of quantities carried by drops (e.g. solute), and any formal order of accuracy in bin resolution and time, while maintaining conservation of mass. Appropriate choices of (1) and (2) result in schemes that are more efficient than the popular Bott (1998) and Tzivion et. al. (1987) schemes, as measured by the computational cost required to attain a given level of accuracy. This approach can be extended to collisional breakup and to collisional processes involving ice or aerosol particles.