Scientific journal
Scientific Review. Technical science
ISSN 2500-0799
ПИ №ФС77-57440

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MATHEMATIC MODEL AND NUMERICAL TECHNIQUE FOR INVESTIGATION DIFFUSION AND HEAT CONDUCTION PHENOMENA

Gubarev S.V. 1 Berg D.B. 2 Dobrjak P.V. 2
1 Institute of Industrial Ecology Ural branch of RAS
2 Federal State Autonomous Education Institution of Higher Professional Education «Ural Federal University named after the first President of Russia B.N.Yeltsin»
This article describes mathematic model and numerical method for partial parabolic differential equations of diffusion and heat conduction phenomena. Describes common numerical methods for solving differential equations parabolic type. Cellular Automata as numerical method for partial parabolic equation is described. Original Cellular Automata Margolis diffusion rule gives a discrete distribution. Described 2D and 3D Margolis mathematic model diffusion allows to get continuous distribution of physical parameter. Mathematic model Cellular Automata for molecular diffusion was verified by compared with analytical decision of diffusion equation. Relative error calculated of modified mathematical model and was about one percent. The diffusion coefficients are calculated dimensionless for modified mathematic model.