2020
DOI: 10.1016/j.jcp.2020.109233
|View full text |Cite
|
Sign up to set email alerts
|

Positivity-preserving finite volume scheme for compressible two-phase flows in anisotropic porous media: The densities are depending on the physical pressures

Abstract: We are concerned with the approximation of solutions to a compressible two-phase flow model in porous media thanks to an enhanced control volume finite element discretization. The originality of the methodology consists in treating the case where the densities are depending on their own pressures without any major restriction neither on the permeability tensor nor on the mesh. Contrary to the ideas of [23], the point of the current scheme relies on a phaseby-phase "sub"-unpwinding approach so that we can recov… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1

Citation Types

0
7
0

Year Published

2020
2020
2023
2023

Publication Types

Select...
6
1

Relationship

4
3

Authors

Journals

citations
Cited by 14 publications
(7 citation statements)
references
References 27 publications
0
7
0
Order By: Relevance
“…Yet, consistency or convergence is valid when a numerical assumption holds. Recently, a few convergent positive schemes were designed and analyzed for degenerate parabolic equations with anisotropy, see for instance [13,28,27,40]. The methodology used in these references is accurate of first order for the diffusion since the idea is based on an upwinding strategy of Godunov type.…”
mentioning
confidence: 99%
“…Yet, consistency or convergence is valid when a numerical assumption holds. Recently, a few convergent positive schemes were designed and analyzed for degenerate parabolic equations with anisotropy, see for instance [13,28,27,40]. The methodology used in these references is accurate of first order for the diffusion since the idea is based on an upwinding strategy of Godunov type.…”
mentioning
confidence: 99%
“…It was observed that the accuracy is reduced when the solution is only continuous. Their extensions to complex flows in porous media have been investigated in [7,19]. Contrary to upwind baseddiscretizations, central positive nonlinear schemes have been proposed in [9,25,27].…”
Section: Literature Workmentioning
confidence: 99%
“…It has been extended to a chemotaxis system [22] and to a compressible two-phase flows problem [18]. A slightly improvement was proposed in [19] where the upwinding is taken place only if necessary. However, under some circumstances, both methodologies lack robustness since they induce an important numerical diffusion as the anisotropic ratio becomes important.…”
Section: Introductionmentioning
confidence: 99%
“…The first objective of this work is to devise and investigate an improved positive finite volume discretization for diffusion equations by extending the ideas of [8,19]. In the present paper, the employed technique is generic on finite volume schemes that could be written using the two points like structure [11,16,28].…”
mentioning
confidence: 99%