Dimensional lattice Boltzmann method for transport phenomena simulation without conversion to lattice units

It is proposed a dimensional Lattice Boltzmann Method (LBM) of wide application for simulating fluid flow and heat transfer problems. The proposed LBM consists in the numerical solution of the discrete lattice Boltzmann equation (LBE) using directly the variables in physical units, without the necessity of employing any particular unit conversion system. This includes the integration of LBE in the discrete physical domain using the spatial and time intervals and all the involved quantities in physical units. The dimensional LBM is proposed for both the single and multiple relaxation time schemes, considering the BGK and MRT collision operators, respectively. Several simple tests problems treating different physical phenomena such as one dimensional heat diffusion with source term, two dimensional forced convection with developed and developing flow in a channel under an oscillating and constant heat flux, two-phase stationary bubble in a liquid phase and two-phase dynamic layered Poiseuille flow, both under very high density and viscosity ratios, are simulated. All the numerical solutions were compared with analytical solutions, when available, or with finite difference solutions, otherwise, showing a very good agreement. The proposed method was also compared with the traditional LBM for the treated problems, showing the same accuracy. Besides the simulation of the applied problems employing physical units directly, the proposed LBM allowed the solution of transport phenomena for more severe operational conditions. This includes the simulation of the two multiphase problems with liquid/gas density and gas/liquid kinematic viscosity ratios of about 43300 and 470 respectively, employing the Allen-Canh phase field model. With base on the obtained results it is estimated that the proposed method could enhance the LBM use as simulation tool.