The purpose of this paper is to present a numerical model for immiscible incompressible two-fluid flows, which preserves the discrete mass of the fluid more highly. This method is derived from the variational formulation including the flux-free constraint for the Navier-Stokes equations by the Lagrange multiplier technique and is implemented by the level set of the pseudo-density function, so that we aldo solve the transport equation by the finite element method. Finally we give some numerical results to validate our proposed method
