Modeled lattice boltzmann equation and the constant-density assumption

An approach is proposed to recover the incompressible NS equation based on a constant-density assumption. It is observed that the recovered NS equation is identical to the continuum equation. The constant-density assumption can be used to evaluate the pressure and there is no need to postulate a density distribution function or to assume that density is related to density. A splitting method similar to Toro's proposal is used to solve the Lattice-Boltzmann Equation (LBE) where simulations are validated against 2-D unsteady flow problems. The starting point of the present formulation is the unsteady incompressible isothermal NS equation. The objective of the approach is to recover the first and second equation from a BGK-type modeled BE.