Achieving thermodynamic consistency in a class of free-energy multiphase lattice Boltzmann models

The free-energy lattice Boltzmann (LB) model is one of the major multiphase models in LB community. present study focused on a class which divergence thermodynamic pressure tensor or its equivalent form expressed by chemical potential incorporated into equation via forcing term. Although this may be thermodynamically consistent at continuum level, it suffers from inconsistency discrete level owing to numerical errors [Guo et al., Physical Review E 83, 036707 (2011)]. error term mainly includes two parts, comes gradient operator and other can identified high-order Chapman-Enskog analysis. In paper, we propose an improved scheme eliminate aforementioned models. constructed modifying state standard equation, through discretization $\nabla \left( {\rho c_{\rm{s}}^{\rm{2}}} \right)$ no longer involved force calculation then significantly reduced. Numerical simulations are subsequently performed validate proposed scheme. results show that capable eliminating reduce spurious currents comparison with forcing-based model.