Phase-field-lattice Boltzmann flux solver for simulations of solid-liquid phase change

A phase-field-lattice Boltzmann flux solver (PF-LBFS) is proposed in this paper for numerical simulations of the solid liquid phase change in a pure material. LBFS serves as a flow solver, which globally resolves the Navier-Stokes equations and reconstructs numerical fluxes with local solutions to the lattice Boltzmann equation on the cell interface. Being a physical reconstruction strategy, the LBFS simultaneously reconstructs the inviscid and viscous numerical fluxes and ensures consistency between the local equation resolved on the cell interface and the global governing equations. Another key module of the PF-LBFS is the phase-field equation, which updates the order parameter for identifying the solid-liquid interface. The phase-field method allows a smooth transition between phases and is consolidated into the energy conservation law. The convergence, accuracy, and physical robustness of the proposed method, as well as its flexibility on a nonuniform mesh, are numerically validated through three representative benchmark tests.