Progress in the development of a new lattice Boltzmann method

•A new LBM that remedies four inadequacies of conventional LBM is formulated.•It requires only a relaxation time scale of the flow and fluid properties as inputs.•It is solved with finite difference splitting on minimal D2Q9 and D3Q13 lattices.•It simulates a wide ranges of flow problems with different fluid media correctly.•Its solutions agree excellently with existing experimental and numerical results. A new modeled Boltzmann equation (MBE) with four improvements made to conventional MBE is formulated. The first improvement is to include the particle internal rotational degree of freedom in the derivation of a continuous equilibrium velocity distribution function f eq; thus, rendering the MBE applicable to diatomic gas. The second improvement is made in the expansion assumed for fαeq in the lattice Boltzmann equation (LBE). This expansion is expressed in terms of the particle velocity vector (ξ) alone; hence, the LBE is no longer limited by a very low Mach number (M) assumption, and it also allows the LBE to correctly satisfy the zero divergence of the velocity field for incompressible flow. The third improvement is made to eliminate the bounce-back rule used to model no-slip wall boundary condition for fα because the rule leads to leakage at solid walls and mass conservation is compromised. The fourth improvement is carried out to render the modeled LBE truly valid for hydrodynamic flow simulation. Thus improved, the new lattice Boltzmann method (LBM) is no longer subject to the M