| Abstract: | In this work, we proposed a diffuse-interface model for the dendritic growth
with thermosolutal convection. In this model, the sharp boundary between the fluid
and solid dendrite is firstly replaced by a thin but nonzero thickness diffuse interface,
which is described by the order parameter, and the diffuse-interface based governing
equations for the dendritic growth are presented. To solve the model for the dendritic
growth with thermosolutal convection, we also developed a diffuse-interface multi-relaxation-time lattice Boltzmann (LB) method. In this method, the order parameter
in the phase-field equation is combined into the force caused by the fluid-solid interaction, and the treatment on the complex fluid-solid interface can be avoided. In addition, four LB models are designed for the phase-field equation, concentration equation, temperature equation and the Navier-Stokes equations in a unified framework.
Finally, we performed some simulations of the dendritic growth to test the present
diffuse-interface LB method, and found that the numerical results are in good agreements with some previous works. |
