年間 4 号発行
ISSN 印刷: 2152-2057
ISSN オンライン: 2152-2073
Indexed in
AVERAGING THE NONSTATIONARY EQUATIONS OF VISCOUS SUBSTANCE FILTRATION THROUGH A RIGID POROUS MEDIUM
要約
The asymptotic averaging technique is used to solve the equations describing filtration of viscous compressible barotropic substance in a medium with a periodic structure of pores. As the equation of motion, we consider generalization of the Brinkman equation to the case of a possible unsteady flow of a fluid, which takes into account the nonlinear effects related to the dependence of the viscosity and friction coefficients on pressure. The effective permeability tensor is found in the course of solution on the periodicity cell of the corresponding problems and their subsequent averaging. The results of analytical and numerical-analytical solutions of the problem on a cell in one- and three-dimensional cases, respectively, are presented. The distributions of pressure and velocity in zero approximation are found by solving an averaged macroscopic equation. The effect of different types of dependences of viscosity and friction coefficients on pressure, as well as different types of barotropic relations between density and pressure is investigated.
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Artamonova Nina B., Sheshenin Sergey V., Finite element implementation of a geometrically and physically nonlinear consolidation model, Continuum Mechanics and Thermodynamics, 2022. Crossref