An unconditionally energy stable method for binary incompressible heat conductive fluids based on the phase-field model

This paper proposes an unconditionally energy stable method for incompressible heat conductive fluids under the phase-field framework. We combine the complicated system by the Navier-Stokes equation, Cahn-Hilliard equation, and heat transfer equation. A Crank-Nicolson type scheme is employed to discretize the governing equation with the second-order temporal accuracy. The unconditional energy stability of the proposed scheme is proved, which means that a significantly larger time step can be used. The Crank-Nicolson type discrete framework is applied to obtain the second-order temporal accuracy. We perform the biconjugate gradient method and Fourier transform method to solve the discrete system. Several computational tests are performed to show the efficiency and robustness of the proposed method.