Three models for two phase flow in porous media. (English) Zbl 1430.76447
Summary: We compare three different models of two phase flow in a porous medium; the standard Darcy/Buckley-Leverett model, the Brinkman model and the Helmholtz model. These three models are all singular perturbations of the inviscid Darcy model, and thus have the same formal limits. The existence of such limits have not been proved mathematically, and in this paper we investigate numerically whether limits exist, and whether they are similar.
MSC:
| 76S05 | Flows in porous media; filtration; seepage |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 35L65 | Hyperbolic conservation laws |
| 35Q35 | PDEs in connection with fluid mechanics |
| 76T99 | Multiphase and multicomponent flows |
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