The main objective of the present work is to further investigate the solution of the coupled system (without any time-splitting approach) by means of a preconditioned BiCGstab(2) solver. We obtain high performance with a new preconditioning strategy that combines a triangular block preconditionning for the velocity block with a pressure convection diffusion (PCD) preconditionner for the Schur complement. To provide the stability of the numerical scheme in the presence of high density and viscosity ratios, we use an algebric momentum preserving mass and momentum transport in the conservative form of discrete equations. The consistency between mass and momentum advection is achieved by resolving a new auxiliary continuity equation, using fifth-order WENO scheme and third Runga-Kutta SSP time integrator.