Open AccessNon-isothermal filtration of a viscous compressible fluid in a viscoelastic porous medium
Author(s) -
Rudolf Virts,
A. A. Papin,
M. A. Tokareva
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1666/1/012041
Subject(s) - porous medium , compressibility , mechanics , viscoelasticity , isothermal process , conservation law , viscous liquid , darcy's law , boundary value problem , filtration (mathematics) , conservation of mass , darcy–weisbach equation , mathematics , porosity , physics , thermodynamics , mathematical analysis , geology , geotechnical engineering , statistics
The system of equations of one-dimensional unsteady fluid motion in a viscous heat-conducting medium is considered. The mathematical model is based on the equations of conservation of mass for liquid and solid phases, Darcy’s law, rheological relation, the law of conservation of balance of forces and the equation for the temperature of the medium. The transition to Lagrange variables in the case of an incompressible fluid allows us to reduce the initial system of governing equations to a third-order equation for porosity and a second-order equation for temperature, respectively. A calculation algorithm is proposed and a numerical study of the obtained initial - boundary value problem is carried out.