We propose two mass and heat energy conservative, unconditionally stable, decoupled numerical algorithms for solving the Cahn-Hilliard-Navier-Stokes-Darcy-Boussinesq system that models thermal convection of two-phase flows in superposed free flow and porous media. The schemes totally decouple the computation of the Cahn-Hilliard equation, the Darcy equations, the heat equation, the Navier-Stokes equations at each time step, and thus significantly reducing the computational cost. We rigorously show that the schemes are conservative and energy-law preserving. Numerical results are presented to demonstrate the accuracy and stability of the algorithms.
W. Chen et al., "Conservative Unconditionally Stable Decoupled Numerical Schemes for the Cahn-Hilliard-Navier-Stokes-Darcy-Boussinesq System," Numerical Methods for Partial Differential Equations, Wiley, Sep 2021.
The definitive version is available at https://doi.org/10.1002/num.22841
Mathematics and Statistics
Early View: Online Version of Record before inclusion in an issue
Keywords and Phrases
Convection; Phase Field Model; Two-Phase Flow; Unconditional Stability
International Standard Serial Number (ISSN)
Article - Journal
© 2021 The Authors, All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
10 Sep 2021