A numerical scheme for two-scale phase-field models in porous media

[EN] We consider the flow of two immiscible fluid phases in a porous medium. At the scale of pores, the two fluid phases are separated by interfaces that are transported by the flow. Furthermore, the surface tension at such interfaces depends on the concentration of a surfactant dissolved in one of the fluids. Here we discuss a two-scale model for two-phase porous-media flow, in which concentration-dependent surface tension effects are incorporated. The model is obtained by employing formal homogenization methods and relies on the phase-field approach, in which thin, diffuse interface regions approximate the interfaces. We propose a two-scale numerical scheme and present numerical results revealing the influence of various quantities on the averaged behaviour of the system.