A phase-field Lattice Boltzmann method for liquid-vapor phase change problems based on conservative Allen-Cahn equation and adaptive treegrid

A phase-field Lattice Boltzmann method (LBM) based on Allen-Cahn (A-C) equation with a modified adaptive mesh refinement (AMR) method is presented to simulate the liquid-vapor phase change problem. Three Lattice Boltzmann equations are solved: one for the conservative Allen-Cahn equation, one for the incompressible Navier-Stokes equations, and one for the energy equation. These three equations are written in the form of multiple-relaxation-time, together with the equilibrium and forcing terms using the set of Hermite polynomials. The adaptive mesh refinement technique with quadtree grid data structure is implemented to capture the liquidvapor interface in simulations, in which the mesh can be locally refined by subdividing blocks identified by userdefined criterion. The Lax-Wendroff finite-difference scheme is adopted to calculate the whole computational domain continuously under nonuniform grids. The present method is validated by the classical Stefan problem and then performed to simulate the film boiling heat transfer. The numerical experiments verify the ability of the proposed method to capture the correct evolution of the interface, guarantee the numerical accuracy and remarkably save the computational cost.