The author offers a method (PGRM) of numerical-analytical solving the equation system in partial derivatives describing the natural thermal convection in the complicated-shaped dimensional cavity with arbitrary boundary conditions. The new approach is based on a combination of Petrov – Galerkin method and R-functions (Rvachev functions) and makes it possible to obtain temperature, vortex and current functions satisfying the boundary condi-tions in the form of expansions in certain bases. The coordinated choice of bases provides a natural way to approximate the boundary conditions for the flow function. Unsteady convec-tion problems are solved by combining PGRM and Rothe method.
Basarab M. Numerical-analytical method of solving two-dimensional problems of natural convection in a closed cavity. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 18-35