Study of a numerical scheme for miscible two‐phase flow in porous media

Eymard, Robert; Schleper, Veronika

doi:10.1002/num.21823

Cited by 4 publications

(1 citation statement)

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“…• the approximation of two-phase flow in porous media, with dissolution or heterogeneous capillary curves [4,15,16] Note also that it is easy to implement an upstream weighting scheme for a convection term together with the TP scheme, which ensures more stability. The main drawback is that the admissible meshes in this case are restricted, especially in the 3D case, since we require the orthogonality condition for the TP scheme to be consistent.…”

Section: Discussionmentioning

confidence: 99%

TP or not TP, that is the question

Eymard¹,

Gallouët

Guichard

et al. 2014

Comput Geosci

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We give here a comparative study of the mathematical analysis of two (classes of) discretisation schemes for the computation of approximate solutions to incompressible two phase flow problem in homogeneous porous media. The first scheme is the well-known finite volume scheme with a two-point flux approximation, classically used in industry. The second class contains the so-called approximate gradient schemes, which include finite elements with mass lumping, mixed finite elements, mimetic finite differences. Both (classes of) schemes are nonconforming and can be expressed using discrete function and gradient reconstructions within a variational formulation. Each class has its specific advantages and drawbacks: monotony properties are natural with the two point finite volume scheme, but meshes are restricted due to consistency issues; on the contrary, gradient schemes can be used on general meshes, but monotony properties are difficult to obtain.

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Section: Discussionmentioning

confidence: 99%