On the results of testing some algorithms for calculating coagulation processes in dispersed systems

The object of the study is coagulation processes in clouds, which are a complex thermo-hydrodynamic and microphysical system characterized by unsteadiness, three-dimensionality and nonlinearity. These features make numerical modeling the main method of studying the evolution of clouds both in natural conditions and under active influence, which increases the requirements for the effectiveness of the numerical methods used, such as stability, convergence and cost-effectiveness. The development or selection of methods that meet these requirements necessitates careful research, including preliminary testing of these methods by comparing the results of calculations of test problems with their exact solutions. The study is based on the analysis of Cauchy test problems for kinetic (integrodifferential) equations and systems of kinetic (integrodifferential) coagulation equations in single-phase and two-phase spatially homogeneous dispersed systems. In the course of the work, it was found that the numerical solutions obtained using the Bubnov-Galerkin method and the developed iterative matrix method, which is a modification of the finite difference method, are in good agreement with the analytical solutions. These methods have demonstrated their applicability for modeling coagulation processes in mixed dispersed systems, including convective (hail) clouds. The high accuracy of the results of the numerical solution of the test problem related to coagulation processes in a dispersed medium, based on the results of the study, allows us to conclude that the Bubnov-Galerkin method and the iterative matrix method can be used to study microphysical processes in convective clouds. Numerical experiments based on these methods open up prospects for modeling the processes of cloud formation and development both in natural conditions and under active exposure, including drawing on the experience gained in previous research by other specialists in the field.