Numerical Study of a Problem of Fluid Filtration in a Thin Poroelastic Layer
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.Downloads
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