Finite Volume Element Approximations of Nonlocal in Time One-Dimensional Flows in Porous Media

Computing ◽  
2000 ◽  
Vol 64 (2) ◽  
pp. 157-182 ◽  
Author(s):  
R. E. Ewing ◽  
R. D. Lazarov ◽  
Y. Lin
Keyword(s):  
Porous Media ◽  
Finite Volume ◽  
Volume Element ◽  
One Dimensional ◽  
Flows In Porous Media ◽  
Finite Volume Element

scholarly journals A Fully Discrete Symmetric Finite Volume Element Approximation of Nonlocal Reactive Flows in Porous Media

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Zhe Yin ◽  
Qiang Xu
Keyword(s):  
Porous Media ◽  
Finite Volume ◽  
Volume Element ◽  
Optimal Order ◽  
Element Approximation ◽  
Two Dimensional ◽  
Reactive Flows ◽  
Flows In Porous Media ◽  
Fully Discrete ◽  
Finite Volume Element

We study symmetric finite volume element approximations for two-dimensional parabolic integrodifferential equations, arising in modeling of nonlocal reactive flows in porous media. It is proved that symmetric finite volume element approximations are convergent with optimal order inL2-norm. Numerical example is presented to illustrate the accuracy of our method.

scholarly journals Modified Method of Characteristics Combined with Finite Volume Element Methods for Incompressible Miscible Displacement Problems in Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Sarvesh Kumar ◽  
Sangita Yadav
Keyword(s):  
Porous Media ◽  
Finite Volume ◽  
Method Of Characteristics ◽  
Miscible Displacement ◽  
Volume Element ◽  
Modified Method ◽  
Finite Volume Element ◽  
Velocity Equation ◽  
Modified Method Of Characteristics ◽  
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. 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.

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

2013 ◽  
Vol 04 (03) ◽  
pp. 1350013 ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document