Abstract
The paper presents results of a numerical study of a mathematical model of viscous fluid filtration in a poroelastic medium with viscoelastic properties. The focus of this research is on model development, problem formulation, and elaboration of a numerical algorithm to solve this problem, as well as a preliminary analysis of numerical study results. The proposed model can be used in a study of processes that occur in the ice cover. This approach treats the ice as a biphasic medium consisting of a liquid (water) phase and a solid (ice) phase being a solid elastic ice skeleton with viscoelastic properties. Thus, the ice cover has properties of a non-Newtonian fluid in this model, and phase transitions and temperature changes are out of concern. A small time parameter is introduced for the process of nondimensionalizing of the original equation system. After passing to the limit (for slow processes), the equation system describes the solid skeleton as a medium with elastic properties greater than viscous. Test numerical calculations are performed, and the field of velocities, porosity, and critical stress values are obtained.
Highlights
Излагаются результаты численного исследования математической модели фильтрации вязкой жидкости в пороупругой среде, обладающей вязкоупругими свойствами
The focus of this research is on model development, problem formulation, and elaboration of a numerical algorithm to solve this problem, as well as a preliminary analysis of numerical study results
The proposed model can be used in a study of processes that occur in the ice cover
Summary
Законы сохранения масс для жидкости и твердой фазы в отсутствие фазовых переходов выглядят следующим образом [1]:. Где t – время, ρf – плотность жидкости, ρs – плотность твердого скелета, vf , vs – скорости жидкой и твердой фаз соответственно,. Где K – коэффициент фильтрации, pf – давление жидкости, g – плотность массовых сил. Где ρ = (1 − φ)ρs + φρf – средняя плотность среды, σ = σs(1 − φ) + σf φ – общее напряжение, определенное как средневзвешенное, ptot = φpf + (1 − φ)ps – общее давление, ν – динамическая вязкость твердой среды. В работе [12] рассмотрены различные режимы движения в зависимости от поведения возникающего в задаче малого параметра. Как частный случай рассмотрим задачу для уравнений (6), (10), (11), дополненных следующими начально-краевыми условиями:.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
