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

•A numerical framework is proposed for solving the Cahn-Hilliard-Navier-Stokes system.•The proposed schemes decouple the velocity field and the phase variables.•The proposed schemes obey an energy dissipation law in the original variables.•The proposed methodology can be applied to other hydrodynami...

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