Abstract: The article is devoted to a theoretical study of a non-stationary problem on thermomechanical processes in snow with account of effects of melting and freezing. Snow is modeled as a continuous three-phase medium consisting of water, air and porous ice skeleton. The filtration process in snow is described by the mass balance equations for each of the three phases, Darcy's equations for the two-phase `air-water' component, and the single-temperature heat balance equation for the three-phase medium. For this model, the hypotheses are accepted that the ice skeleton is an immovable absolutely rigid body, the ice skeleton porosity is a given function of temperature, and the genuine densities of the distinct phases are constant. With account of these hypotheses, the full model reduces to a strongly nonlinear elliptic-parabolic system with additional kinetic equation linking porosity of ice skeleton to intensity of the phase transition. For the one-dimensional setting, the Rothe scheme is constructed as an approximation of the considered problem and the Rothe method is formally justified, i.e., convergence of approximate solutions to the solution of the considered problem is established under some additional regularity requirements.

Cite: Alekseeva S.V. , Sazhenkov S.A.
Studying the Model of Air and Water Filtration in a Melting or Freezing Snowpack
Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software. 2022. V.15. N2. P.5-16. DOI: 10.14529/mmp220201 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:

Aug 23, 2021

Identifiers:

Web of science:	WOS:000864271000001
Scopus:	2-s2.0-85143064432
Elibrary:	49307944
OpenAlex:	W4312547131

Citing:

DB	Citing
Scopus	1
Web of science	1

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