Abstract
The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations, the pressure-velocity equation and the concentration equation. In this paper, we present a mixed finite volume element method (FVEM) for the approximation of the pressure-velocity equation. Since modified method of characteristics (MMOC) minimizes the grid orientation effect, for the approximation of the concentration equation, we apply a standard FVEM combined with MMOC. A priori error estimates in L∞(L2) norm are derived for velocity, pressure and concentration. Numerical results are presented to substantiate the validity of the theoretical results.
Highlights
A mathematical model describing miscible displacement of one incompressible fluid by another in a horizontal porous medium reservoir Ω ⊂ R2 with boundary ∂Ω of unit thickness over a time period of J = (0, T] is given by u = − κ μ (x) (c) ∇p∀ (x, t) ∈ Ω × J, (1)∇ ⋅ u = q ∀ (x, t) ∈ Ω × J, (2) φ (x) ∂c ∂t
The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations, the pressure-velocity equation and the concentration equation
We present a mixed finite volume element method (FVEM) for the approximation of the pressure-velocity equation
Summary
Douglas et al [4, 5], Ewing and Wheeler [6], and Darlow et al [7] have discussed the mixed finite element method for approximating the velocity as well as pressure and a standard Galerkin method for the concentration equation. They have derived optimal error estimates in L∞(L2) norm for the velocity and concentration.
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