On the control volume finite element methods and their applications to multiphase flow

Zhangxin Chen; Zhangxin Chen

doi:10.3934/nhm.2006.1.689

Networks and Heterogeneous Media

2006, Volume 1, Issue 4: 689-706. doi: 10.3934/nhm.2006.1.689

Previous Article Next Article

On the control volume finite element methods and their applications to multiphase flow

Zhangxin Chen ^{1
,}

1.
Department of Mathematics, Box 750156, Southern Methodist University, Dallas, TX 75275-0156

Received: 01 September 2006
Primary: 65N30, 65N10; Secondary: 76S05, 76T05.

In this paper we systematically review the control volume finite element (CVFE) methods for numerical solutions of second-order partial differential equations. Their relationships to the finite difference and standard (Galerkin) finite element methods are considered. Through their relationship to the finite differences, upstream weighted CVFE methods and the conditions on positive transmissibilities (positive flux linkages) are studied. Through their relationship to the standard finite elements, error estimates for the CVFE are obtained. These estimates are comparable to those for the standard finite element methods using piecewise linear elements. Finally, an application to multiphase flows in porous media is presented.
- Control volume finite element,
- Galerkin finite element,
- error analysis,
- upstream weighting,
- multiphase flow,
- numerical experiments
Citation: Zhangxin Chen. On the control volume finite element methods and their applications to multiphase flow[J]. Networks and Heterogeneous Media, 2006, 1(4): 689-706. doi: 10.3934/nhm.2006.1.689

Related Papers:
Abstract

In this paper we systematically review the control volume finite element (CVFE) methods for numerical solutions of second-order partial differential equations. Their relationships to the finite difference and standard (Galerkin) finite element methods are considered. Through their relationship to the finite differences, upstream weighted CVFE methods and the conditions on positive transmissibilities (positive flux linkages) are studied. Through their relationship to the standard finite elements, error estimates for the CVFE are obtained. These estimates are comparable to those for the standard finite element methods using piecewise linear elements. Finally, an application to multiphase flows in porous media is presented.
Reader Comments

Your name:*

Email:*
© 2006 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)