Abstract:

The dissertation presents methods, software packages, and results of numerical research of two mathematical models of evolutionary physical processes described by initial-boundary value problems for systems of nonlinear partial differential equations. Numerical investigation of both models requires the massive calculations in a wide range of model parameters to find conditions for adequate reproduction of the time-dependent characteristics observed in the experiment. Such studies take significant expenditures of computer resources and make it necessary to use parallelism to improve computing performance. The first model is the polaron model of the hydrated electron formation; the second one is a model of the passage of multicomponent hydrocarbon gas-condensate mixtures through a porous medium. Mathematical statements of problems have been formulated for these models, computational schemes have been constructed, problem-oriented computer codes have been created using MPI parallel programming technology. In both models, calculations of time-dependent quantities characterizing the dynamics of the processes under study were carried out. The reasonable agreement of numerical results with the corresponding experimental data confirms the adequacy of the approaches used and the prospects for their further use and development.

(based on the PhD thesis)