A MCC finite element approximation of incompressible miscible displacement in porous media

Abstract

Available online xxxx Keywords: Characteristic method Mixed finite element method Mass conservation Incompressible miscible displacement Continuous flux Error estimate a b s t r a c tIn this paper, we analyze an efficient numerical scheme for the coupled system of incompressible miscible displacement in porous media. Mass-conservative characteristic finite element is used for concentration equation, which continuous velocities are needed. Therefore we solve flow equation by mixed finite element method with continuous flux approximation. Then we show this scheme preserves the mass balance identity and optimal l ∞ (L 2 ) error estimate of the concentration. Numerical experiments are given to confirm the convergence and the property of mass balance.

Simplified finite element algorithm to solve conjugate heat and mass transfer in porous medium

“…In this process, one must be aware of two fundamental points: first, it does not calculate exact solutions but approximate ones; second, it discretizes the problem by representing functions by a finite number of values, that is, to move from the “continuous” to the “discrete”. There are numerous methods for the numerical approximation of PDEs, among them, popularly adopted are finite element method (Lewis and Garner, 1972; Strada and Lewis, 1980; Morgan et al , 1984; Tadayon et al ,1987; Ahmed et al , 2011; Ahmed et al , 2009; Badruddin et al , 2006a, 2006b, 2007a, 2007b, 2012a, 2012b, 2012c; Li and Rui, 2015; Sajid et al , 2008; Balla and Kishan, 2015; Wansophark et al , 2005) finite difference method (Achemlal and Sriti, 2015; del Teso, 2014; Oka et al , 1994; Rui and Liu, 2015; Liu and Yuan, 2008; Sheremet and Pop, 2014; Chamkha and Muneer, 2013; Sheremet, 2015) and finite volume method (Dotlić, 2014; Kumar, 2012). These finite element, finite difference and finite volume methods require that each PDE be converted into its equivalent set of algebraic equations that depends on the number of elements into which the physical domain is divided.…”