Geodesic
Numerical simulation of buoyancy-driven flows in complex domains
Matematičeskoe modelirovanie, Tome 8 (1996) no. 1, pp. 103-118.

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The paper deals with the solution of 2D transient problems of free convection in the stream function – vorticity – temperature formulation. For the flows in complex irregular domains there are constructed fixed grid numerical algorithms on the basis of different variants of the fictitious domain method. The initial calculation domain is ducked into a rectangular and a new problem with discontinuous coefficients is considered. The possibilities of this approach are discussed for buoyancy-driven flow prediction in multi-connected domains where an integral constraint is necessary to evaluate the stream function at a boundary. Various schemes are presented to take account the problem peculiarities in the extended domain. Two free convection problems are studied numerically: a flow in a trapezoidal cavity and free convection in a rectangular cavity with an internal body. 
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     author = {P. N. Vabishchevich and V. V. Chudanov and A. G. Churbanov},
     title = {Numerical simulation of buoyancy-driven flows in complex domains},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {103--118},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1996_8_1_a9/}
}
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P. N. Vabishchevich; V. V. Chudanov; A. G. Churbanov. Numerical simulation of buoyancy-driven flows in complex domains. Matematičeskoe modelirovanie, Tome 8 (1996) no. 1, pp. 103-118. http://geodesic.mathdoc.fr/item/MM_1996_8_1_a9/