Onotskyi V. Numerical and computer modeling of transfer processes with application of two-step symmerized algorithms

This thesis is devoted to discrete models for processes of heat and mass transfer such as initial-boundary value problems in mathematical physics with first order time derivative, convection and diffusion terms and for Navier-Stokes equations. For the pointed source identification problem with unknown locations and intensities regularization is done, the method is developed, numerical solution is obtained. New discrete model for Navier-Stokes equations, which describes the process of relief relief, is offered. Developed hopscotch finite-difference algorithm (DS-algorithm) applied to this problem. Stability conditions of DS-algorithm for first order hyperbolic equations of divergence and nondivergence form are obtained. Approximation, dissipation, conservation, transport properties, the influence of artificial viscosity are investigated. DS-algorithms for pseudoparabolic equation and Burger's equation are developed, local stability of finite-difference schemes is proved. Computer models for the process of relief formation and process of the spread of contamination with pointed sources are proposed. Also numerical experiments on the test problems are conducted.