Unconditionally stable numerical methods for Cahn-Hilliard-Navier-Stokes-Darcy system with different densities and viscosities

Gao Y, Han D, He X, Rüde U (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Journal of Computational Physics Elsevier

Book Volume: 454

Article Number: 110968

DOI: 10.1016/j.jcp.2022.110968

Abstract

In this article we consider the numerical modeling and simulation via the phase field approach for coupled two-phase free flow and two-phase porous media flow of different densities and viscosities. The model consists of the Cahn-Hilliard-Navier-Stokes equations in the free flow region and the Cahn-Hilliard-Darcy equations in porous media that are coupled by several domain interface conditions. It is showed that the coupled model satisfies an energy law. Then we first propose a coupled unconditionally stable finite element method for solving this model and analyze the energy stability for this method. Furthermore, based on the ideas of pressure stabilization and artificial compressibility, we propose an unconditionally stable time stepping method that decouples the computation of the phase field variable, the velocity and pressure of free flow, the velocity and pressure of porous media, hence significantly reduces the computational cost. The energy stability of this decoupled scheme with the finite element spatial discretization is rigorously established. We verify numerically that our schemes are convergent and energy-law preserving. Numerical experiments are also performed to illustrate the features of two-phase flows in the coupled free flow and porous media setting.

Authors with CRIS profile

Ulrich Rüde Lehrstuhl für Informatik 10 (Systemsimulation)

Involved external institutions

Northwestern Polytechnical University / 西北工业大学 (NPU/NWPU) CN China (CN) Missouri University of Science and Technology US United States (USA) (US)

How to cite

APA:

Gao, Y., Han, D., He, X., & Rüde, U. (2022). Unconditionally stable numerical methods for Cahn-Hilliard-Navier-Stokes-Darcy system with different densities and viscosities. Journal of Computational Physics, 454. https://dx.doi.org/10.1016/j.jcp.2022.110968

MLA:

Gao, Yali, et al. "Unconditionally stable numerical methods for Cahn-Hilliard-Navier-Stokes-Darcy system with different densities and viscosities." Journal of Computational Physics 454 (2022).

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