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

https://doi.org/10.1002/num.22841

Chen, Wenbin; Han, Daozhi; Wang, Xiaoming; Zhang, Yichao (September 2021, Numerical Methods for Partial Differential Equations)

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

https://doi.org/10.1016/j.jcp.2022.110968

Gao, Yali; Han, Daozhi; He, Xiaoming; Rüde, Ulrich (April 2022, Journal of Computational Physics)

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A linear second-order in time unconditionally energy stable finite element scheme for a Cahn–Hilliard phase-field model for two-phase incompressible flow of variable densities

https://doi.org/10.1016/j.cma.2021.114186

Fu, Guosheng; Han, Daozhi (December 2021, Computer Methods in Applied Mechanics and Engineering)

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Second-order decoupled energy-stable schemes for Cahn-Hilliard-Navier-Stokes equations

https://doi.org/10.1016/j.jcp.2021.110536

Zhao, Jia; Han, Daozhi (October 2021, Journal of Computational Physics)

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Existence and weak–strong uniqueness of solutions to the Cahn–Hilliard–Navier–Stokes–Darcy system in superposed free flow and porous media

https://doi.org/10.1016/j.na.2021.112411

Han, Daozhi; He, Xiaoming; Wang, Quan; Wu, Yanyun (October 2021, Nonlinear Analysis)
null (Ed.)
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Error estimate of a decoupled numerical scheme for the Cahn–Hilliard–Stokes–Darcy system

Wenbin Chen; Shufen Wang; Yichao Zhang; Daozhi Han; Cheng Wang; Xiaoming Wang (June 2021, IMA journal of numerical analysis)

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Dynamic Transitions and Bifurcations for a Class of Axisymmetric Geophysical Fluid Flow

https://doi.org/10.1137/20M1321139

Han, Daozhi; Hernandez, Marco; Wang, Quan (January 2021, SIAM Journal on Applied Dynamical Systems)
null (Ed.)
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Dynamic transitions and bifurcations for thermal convection in the superposed free flow and porous media

https://doi.org/10.1016/j.physd.2020.132687

Han, Daozhi; Wang, Quan; Wang, Xiaoming (December 2020, Physica D: Nonlinear Phenomena)
null (Ed.)
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Uniquely Solvable and Energy Stable Decoupled Numerical Schemes for the Cahn–Hilliard–Navier–Stokes–Darcy–Boussinesq System

https://doi.org/10.1007/s10915-020-01341-7

Chen, Wenbin; Han, Daozhi; Wang, Xiaoming; Zhang, Yichao (November 2020, Journal of Scientific Computing)
null (Ed.)
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A second order, linear, unconditionally stable, Crank–Nicolson–Leapfrog scheme for phase field models of two-phase incompressible flows

https://doi.org/10.1016/j.aml.2020.106521

Han, Daozhi; Jiang, Nan (October 2020, Applied Mathematics Letters)

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