Uniquely Solvable and Energy Stable Decoupled Numerical Schemes for the Cahn-Hilliard-Navier-Stokes-Darcy-Boussinesq System
In this article we propose the Cahn-Hilliard-Navier-Stokes-Darcy-Boussinesq system that models thermal convection of two-phase flows in a fluid layer overlying a porous medium. Based on operator splitting and pressure stabilization we propose a family of fully decoupled numerical schemes such that the Navier-Stokes equations, the Darcy equations, the heat equation and the Cahn-Hilliard equation are solved independently at each time step, thus significantly reducing the computational cost. We show that the schemes preserve the underlying energy law and hence are unconditionally long-time stable. Numerical results are presented to demonstrate the accuracy and stability of the algorithms.
W. Chen et al., "Uniquely Solvable and Energy Stable Decoupled Numerical Schemes for the Cahn-Hilliard-Navier-Stokes-Darcy-Boussinesq System," Journal of Scientific Computing, vol. 85, no. 2, Springer, Nov 2020.
The definitive version is available at https://doi.org/10.1007/s10915-020-01341-7
Mathematics and Statistics
Center for High Performance Computing Research
Keywords and Phrases
Convection; Phase field model; Two-phase flow; Unconditional stability
International Standard Serial Number (ISSN)
Article - Journal
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01 Nov 2020