Computing numerical solutions of the pseudo-parabolic Buckley–Leverett equation with dynamic capillary pressure

Eduardo Abreu and Jardel Vieira

Mathematics and Computers in Simulation (MATCOM), 2017, vol. 137, issue C, 29-48

Abstract: We present numerical approaches for solving a pseudo-parabolic partial differential equation, which models incompressible two phase flow in porous media taking into account dynamic effects in the capillary pressure. First, we briefly discuss two numerical schemes based on the operator splitting technique. Our numerical experiments show that the standard splitting, widely used to solve parabolic problems, may fail when applied to pseudo-parabolic models. As an illustration, we give an example for this case. So we present an operator splitting scheme based on a dispersive-like character that obtains correct numerical solutions. Then, we discuss an unsplit efficient numerical modelling, locally conservative by construction. This framework is based on a fully coupled space–time mixed hybrid finite element/volume discretization approach in order to account for the delicate local nonlinear balance between the numerical approximations of the hyperbolic flux and the pseudo-parabolic term, but linked to a natural dispersive-like character of the full pseudo-parabolic equation. We compare our numerical results with approximate solutions constructed with methods recently introduced in the specialized literature, in order to establish that we are computing the expected qualitative behaviour of the solutions.

Keywords: Pseudo-parabolic equation; Dynamic capillary pressure; Two-phase flow; Hybrid mixed finite element; Porous media (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475416301999
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:137:y:2017:i:c:p:29-48

DOI: 10.1016/j.matcom.2016.10.006

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().