Prokhorov S.A., Ten A.V. Computer Simulations of the Heat Transfer Process in Heterogeneous Media Using Parallel Computing Technologies

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https://doi.org/10.15688/mpcm.jvolsu.2023.3.1

Stanislav A. Prokhorov
Student, Department of Information System and Computer Modeling,
Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Anastasiya V. Ten
Candidate of Sciences (Physics and Mathematics), Associate Professor, Department of Information System and Computer Modeling,
Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. This paper studied a two-dimensional linear equation of thermal conductivity with a fractional differentiation order and compiled a computational algorithm for its numerical solution. Fractional derivatives in space and time were represented using the Riemann—Liouville definition, and the Grunwald— Letnikov definition with a shift was used to approximate them. Based on the computational algorithm, a program was written for computer modeling of the heat exchange process in heterogeneous environments. A version of the program has been developed using OpenMP parallel computing technology. The computer model has been tested by a number of numerical experiments to solve the problem of thermal momentum propagation. Based on the modeling results, the effect of fractional differentiation order on the thermal conductivity process was studied.

Key words: computer modeling, difference schemes, fractional differentiation, thermal equation, parallel calculations.

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Computer Simulations of the Heat Transfer Process in Heterogeneous Media Using Parallel Computing Technologies by Prokhorov S.A., Ten A.V. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Mathematical Physics and Computer Simulation. Vol. 26 No. 3 2023, pp. 26-34

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