In this article, we consider a phase field model with different densities and viscosities for the coupled two-phase porous media flow and two-phase free flow, as well as the corresponding numerical simulation. This model consists of three parts: a Cahn-Hilliard-Darcy system with different densities/viscosities describing the porous media flow in matrix, a Cahn-illiard-Navier-Stokes system with different densities/viscosities describing the free fluid in conduit, and seven interface conditions coupling the flows in the matrix and the conduit. Based on the separate Cahn-Hilliard equations in the porous media region and the free flow region, a weak formulation is proposed to incorporate the two-phase systems of the two regions and the seven interface conditions between them, and the corresponding energy law is proved for the model. A fully decoupled numerical scheme, including the novel decoupling of the Cahn-Hilliard equations through the four phase interface conditions, is developed to solve this coupled nonlinear phase field model. An energy-law preservation is analyzed for the temporal semi-discretization scheme. Furthermore, a fully discretized Galerkin finite element method is proposed. Six numerical examples are provided to demonstrate the accuracy, discrete energy law, and applicability of the proposed fully decoupled scheme.
Y. Gao et al., "Fully Decoupled Energy-stable Numerical Schemes For Two-phase Coupled Porous Media And Free Flow With Different Densities And Viscosities," ESAIM: Mathematical Modelling and Numerical Analysis, vol. 57, no. 3, pp. 1323 - 1354, EDP Sciences; Société de Mathématiques Appliquées et Industrielles, May 2023.
The definitive version is available at https://doi.org/10.1051/m2an/2023012
Mathematics and Statistics
Keywords and Phrases
Cahn-Hilliard-Navier-Stokes-Darcy model; Different densities; Energy stability; Fully decoupled; Karstic geometry; Phase-field model
International Standard Serial Number (ISSN)
Article - Journal
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01 May 2023