Geodesic
Chipashvili. Numeric simulation of heat transfer in anisotropic bodies with discontinuous parameters
Matematičeskoe modelirovanie, Tome 16 (2004) no. 5, pp. 94-102.

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Heat transfer in multi-layer bodies with anisotropic transfer parameters is modeled in this paper. Heat conductivity of each layer is described by a heat conductivity tensor, so at the borders of layer conjugation not only components but also main tensor axes become discontinuous. It was confirmed that on such borders the normal components of heat density vector are continuous as well as a temperature, and the tangential components are discontinuous, what means discontinuity of the vector of heat flow density at the borders, dividing the layers. A confirmation of this fact is extremely needed to declare boundary conditions on such borders properly. A relation for normal component of heat flow vector, useful for economic numerical simulations, is formulated. For this method an economic absolutely stable ADI method with extrapolation, developed by the authors, was applied. Results of numerical simulation are discussed. 
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     author = {V. F. Formalev and S. A. Kolesnik and A. A. Chipashvili},
     title = {Chipashvili. {Numeric} simulation of heat transfer in anisotropic bodies with discontinuous parameters},
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V. F. Formalev; S. A. Kolesnik; A. A. Chipashvili. Chipashvili. Numeric simulation of heat transfer in anisotropic bodies with discontinuous parameters. Matematičeskoe modelirovanie, Tome 16 (2004) no. 5, pp. 94-102. http://geodesic.mathdoc.fr/item/MM_2004_16_5_a7/

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