Methodology of the numerical solution equations system of three-dimensional model convective cloud

A three-dimensional numerical model of a convective cloud is developed taking into account thermodynamic, microphysical and electrical processes. The model uses a detailed microphysics. The system of equations of the cloud model describing the time variation of the dynamic and microphysical characteristics of the cloud consists of 3 equations of motion, heat and moisture balance equations, 137 equations describing the spectrum of cloud droplets, crystals, and microbubble particles. In addition, in order for the solution to satisfy the continuity equation, it is necessary to solve the three-dimensional elliptic equation for the pressure perturbation at each time step. One of the methods widely used for solving such problems is the splitting method developed by G.I. Marchuk, an improved version of this method, the predictor scheme with a divergent corrector, was successfully used in the modeling of cumulus clouds by R. Pastushkov. The conducted studies showed that, despite the certain complexity in the implementation of this scheme, it provides the necessary stability of the count, an approximation of the second order of accuracy in space and time, and is conservative. Splitting methods for physical processes and componentwise splitting are used (locally-one-dimensional schemes). The equations of the cloud model in finite-difference form were approximated by central and directional differences for spatial variables, as well as directed time differences. The resulting algebraic system was solved by a sweep method.