  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.
