Modeling of heat and mass transfer in the discontinuum approximation
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 1, pp. 137-164
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The article presents a theoretical analysis of the governing equations expressing the fundamental conservation laws in the continuum and discontinuum approximations, and methods for solving problems of hydrodynamics as one of the most important subfields of continuum mechanics. This article is an attempt to more accurately describe physicochemical macro-processes. It is shown that the most suitable equations for computer modeling are the conservation laws under natural constraints on the minimum spatial and time scales, i.e., equations without partial derivatives and constraints on the solution smoothness. Using the continuity and thermal conductivity equations, a phenomenological method for constructing and numerically solving the governing equations is presented, and comparison with the traditional approach is given.
Keywords:
continuum medium, Knudsen number, phenomenological approach, mathematical modeling, heat and mass transfer
@article{VUU_2024_34_1_a8,
author = {S. I. Martynenko},
title = {Modeling of heat and mass transfer in the discontinuum approximation},
journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
pages = {137--164},
publisher = {mathdoc},
volume = {34},
number = {1},
year = {2024},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VUU_2024_34_1_a8/}
}
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%0 Journal Article %A S. I. Martynenko %T Modeling of heat and mass transfer in the discontinuum approximation %J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki %D 2024 %P 137-164 %V 34 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/VUU_2024_34_1_a8/ %G ru %F VUU_2024_34_1_a8
S. I. Martynenko. Modeling of heat and mass transfer in the discontinuum approximation. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 1, pp. 137-164. http://geodesic.mathdoc.fr/item/VUU_2024_34_1_a8/