A new mesoscopic scale timestep adjustable non-dimensional lattice Boltzmann method for melting and solidification heat transfer

A mesoscopic scale timestep adjustable non-dimensional lattice Boltzmann method (NDLBM) for fluid flow and heat transfer with solid-liquid phase change is developed using a scaling analysis based on the mesoscopic length and velocity scales. The interface between fluid and solid is treated as a mixture domain with transient porosity distributions and thickness. Timesteps are adjusted by using a transient mesoscopic Mach number independent of mesh size to speed up the computation. The code is validated by comparison of transient Nusselt numbers, isotherms, streamlines, and porosity with prior studies of natural convection in a square enclosure with and without phase change material. A benchmark problem is proposed to obtain the same equilibrium state for both melting and solidification procedures. Full maps of the flow and heat transfer patterns for both melting and solidification are presented based on the key dimensionless governing parameters. The effects of Mach, Stefan (0.01-10), Rayleigh (¹⁰³-¹⁰⁸), and Prandtl (0.1-10) numbers are discussed.