Geodesic
Numerical-analytical method of solving two-dimensional problems of natural convection in a closed cavity
Matematičeskoe modelirovanie i čislennye metody, no. 1 (2014), pp. 18-35 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 conditions 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 convection problems are solved by combining PGRM and Rothe method.
Keywords: natural convection, the method of R-functions, Petrov–Galerkin method. 
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M. A. Basarab. Numerical-analytical method of solving two-dimensional problems of natural convection in a closed cavity. Matematičeskoe modelirovanie i čislennye metody, no. 1 (2014), pp. 18-35. http://geodesic.mathdoc.fr/item/MMCM_2014_1_a2/

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