A regularized system of equations describing a flow of isothermal two-component mixture with diffuse interface is studied. The equation of energy balance and its corollary, i.e., the law of non-increasing of the total energy are derived under general assumptions on the Helmholtz free energy of the mixture. Necessary and sufficient conditions for linearized stability of constant solutions are obtained (in particular case). A difference approximation of the problem is constructed in the two-dimensional periodic case on a nonuniform rectangular grid. The results of numerical experiments demonstrate a qualitative well-posedness of the problem and the applicability of the criterion of linearized stabilization in the original nonlinear formulation.
The paper reviews essential approaches to describe multiphase flow in fractured and fractured porous media at different spatial scales. A DFN type single and two-phase flow models accounting for non-uniform fracture apertures, flow exchange between fractures, capillary and gravity forces are described in details.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.