Improved multi-relaxation time thermal pseudo-potential lattice Boltzmann method with multi-block grid and complete unit conversion for liquid–vapor phase transition

Abstract

In recent years, the thermal pseudo-potential lattice Boltzmann method (LBM) has been widely adopted in numerical simulations of liquid–vapor phase transition systems. However, the unit conversion for thermal pseudo-potential LBM remains incomplete and elusive, and the numerical simulation efficiency is limited by the uniformly single-block grid. In this paper, the dimensionless evolution equations of thermal pseudo-potential LBM with multi-relaxation time operators are derived for the convenience of adopting real physical parameters and improvement of computational efficiency. The energy equation is re-derived and improved for enhanced accuracy and convenience of numerical calculation. Additionally, a more accurate Martin–Hou equation of state for cryogen is adopted and a modified term for surface tension coefficient is improved to confirm that the surface tension coefficient is grid independent. Moreover, a three-layer boundary structure for the coarse grid is proposed to introduce the multi-block grid into the thermal pseudo-potential LBM for taking into account the intermolecular force and internal heat source term. The aforementioned works improve the thermal pseudo-potential LBM and enable efficient and accurate simulation of the liquid–vapor phase transition within the three-dimensional structure with real physical parameters of a specific working fluid. Finally, numerical simulations are adopted to validate the efficiency and accuracy of the proposed improvements for simulating liquid–vapor phase transition.