This paper presents a physically based technique for simulating complex multiphase fluids. This work is motivated by the "stable fluids" method developed by Stam to handle gaseous fluids. We extend this technique to water, which calls for the development of methods for modeling multiphase fluids and suppressing dissipation. We construct a multiphase fluid formulation by combining the Navier-Stokes equations with the level set method. By adopting constrained interpolation profile (CIP)-based advection, we reduce the numerical dissipation and diffusion significantly. We further reduce the dissipation by converting potentially dissipative cells into droplets or bubbles that undergo Lagrangian motion. Due to the multiphase formulation, the proposed method properly simulates the interaction of water with surrounding air, instead of simulating water in a void space. Moreover. the introduction of the non-dissipative technique means that, in contrast 10 previous methods, the simulated water does not unnecessarily lose mass and its motion is not damped to an unphysical extent. Experiments showed that the proposed method is stable and runs fast. It is demonstrated that two-dimensional simulation runs in real-time.