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Evaluation of three lattice Boltzmann models for multiphase flows in porous media. (English) Zbl 1225.76229
Summary: A free energy (FE) model, the Shan-Chen (S-C) model, and the Rothman and Keller (R-K) model are studied numerically to evaluate their performance in modeling two-dimensional (2D) immiscible two-phase flow in porous media on the pore scale. The FE model is proved to satisfy the Galilean invariance through a numerical test and the mass conservation of each component in the simulations is exact. Two-phase layered flow in a channel with different viscosity ratios was simulated. Comparing with analytical solutions, we see that the FE model and the R-K model can give very accurate results for flows with large viscosity ratios. In terms of accuracy and stability, the FE model and the R-K model are much better than the S-C model. Co-current and countercurrent two-phase flows in complex homogeneous media were simulated and the relative permeabilities were obtained. Again, it is found that the FE model is as good as the R-K model in terms of accuracy and efficiency. The FE model is shown to be a good tool for the study of two-phase flows with high viscosity ratios in porous media.

##### MSC:
 76M28 Particle methods and lattice-gas methods 76S05 Flows in porous media; filtration; seepage 65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs 76T30 Three or more component flows
##### Keywords:
lattice Boltzmann; free energy; multicomponent; porous media
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