Sidorov M. Mathematical modeling and numerical analysis of viscous flow in simply and multiply connected domains by the R-functions method

The thesis is devoted to mathematical modeling of viscous fluids flows in simply and multiply connected areas based on the R-functions method. Linear problem (Stock's flow), nonlinear problems as regard to stream function and stream and temperature functions were considered. For the modeling of truss transparent flows in simply connected areas based on the joint use of principle of superposition, method of successive approximations, and structured-variation method a new numerical method has been built and substantiated, new conditions and estimation of convergence order have been achieved. Mathematical model has been modified at the cost of additional integral relations, which provide pressure uniqueness in multiply connected area. These integral re-lations have been used when numerical methods building. Effectiveness of the methods developed is illustrated by a number of computational experiments and comparisons with known computational solutions received with help of other methods.