Viscosity-Splitting scheme for concentration equation of miscible displacement with solute absorption in porous media

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.

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ON THE APPROXIMATION OF INCOMPRESSIBLE MISCIBLE DISPLACEMENT PROBLEMS IN POROUS MEDIA BY MIXED AND STANDARD FINITE VOLUME ELEMENT METHODS

International Journal of Modeling Simulation and Scientific Computing ◽

10.1142/s179396231350013x ◽

2013 ◽

Vol 04 (03) ◽

pp. 1350013 ◽

Cited By ~ 3

Author(s):

SARVESH KUMAR

Keyword(s):

Porous Media ◽

Finite Volume ◽

A Priori ◽

Nonlinear Partial Differential Equations ◽

Coupled System ◽

Miscible Displacement ◽

Volume Element ◽

Finite Volume Element ◽

Velocity Equation ◽

Concentration Equation

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 and a standard FVEM for the concentration equation. A priori error estimates in L∞(L2) are derived for velocity, pressure and concentration. Numerical results are presented to substantiate the validity of the theoretical results.

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A Broken P1-Nonconforming Finite Element Method for Incompressible Miscible Displacement Problem in Porous Media

ISRN Applied Mathematics ◽

10.1155/2013/498383 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Fengxin Chen ◽

Huanzhen Chen

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Porous Media ◽

Piecewise Linear ◽

Miscible Displacement ◽

Triangular Elements ◽

Concentration Equation ◽

Incompressible Miscible Displacement Problem ◽

Approximate Scheme ◽

Element Method

An approximate scheme is defined for incompressible miscible displacement in porous media. This scheme is constructed by using immersed interface finite element method for the pressure equation which is based on the broken P1-nonconforming piecewise linear polynomials on interface triangular elements and utilizing finite element method for the concentration equation. Error estimates for pressure in broken H1 norm and for concentration in L2 norm are presented.

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A Second Order Characteristic Method for Approximating Incompressible Miscible Displacement in Porous Media

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2012/870402 ◽

2012 ◽

Vol 2012 ◽

pp. 1-21

Author(s):

Tongjun Sun ◽

Keying Ma

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Porous Media ◽

Miscible Displacement ◽

Second Order ◽

Material Derivative ◽

Characteristic Finite Element ◽

Derivative Term ◽

Concentration Equation ◽

Element Method

An approximation scheme is defined for incompressible miscible displacement in porous media. This scheme is constructed by two methods. Under the regularity assumption for the pressure, cubic Hermite finite element method is used for the pressure equation, which ensures the approximation of the velocity smooth enough. A second order characteristic finite element method is presented to handle the material derivative term of the concentration equation. It is of second order accuracy in time increment, symmetric, and unconditionally stable. The optimalL2-norm error estimates are derived for the scalar concentration.

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