Conservative unconditionally stable decoupled numerical schemes for the Cahn–Hilliard–Navier–Stokes–Darcy–Boussinesq system

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 co...

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Bibliographic Details
Published in:Numerical methods for partial differential equations 2022-11, Vol.38 (6), p.1823-1842
Main Authors: Chen, Wenbin, Han, Daozhi, Wang, Xiaoming, Zhang, Yichao
Format: Article
Language:English
Subjects:
Algorithms
Boussinesq equations
convection
Fluid flow
Free convection
Free flow
Navier-Stokes equations
phase field model
Porous media
Thermodynamics
two‐phase flow
unconditional stability
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Summary: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.
ISSN:0749-159X
1098-2426
DOI:10.1002/num.22841