Table of Contents
International Journal of Partial Differential Equations
Volume 2014, Article ID 245086, 16 pages
http://dx.doi.org/10.1155/2014/245086
Research Article

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

1Department of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala 695 547, India
2Department of Mathematics, BITS Pilani, Pilani, Jhunjhunu, Rajasthan 333031, India

Received 8 October 2013; Accepted 27 November 2013; Published 19 January 2014

Academic Editor: Yuncheng You

Copyright © 2014 Sarvesh Kumar and Sangita Yadav. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 norm are derived for velocity, pressure and concentration. Numerical results are presented to substantiate the validity of the theoretical results.