Mathematical Averaging of the Coefficients of a System of Elliptic and Parabolic Equations in Continuum Mechanics

Abstract

The problem of averaging the physical parameters (the coefficients of a system of elliptic and parabolic equations) of the continuum mechanics is studied. As an example, we consider the mathematical model of two-phase filtration. A comparative analysis of a numerical solution of the two-phase filtration in two known models averaged over the thickness of oil bed and in three-dimensional reference models is performed. The calculations are made using the linear, quadratic, and cubic initial permeability. All the calculations are performed for five-point and nine-point flooding systems.