Abstract: Based on the multi-viscous-fluid piecewise parabolic method,the Smagorinsky and Vreman subgrid eddy viscosity models were employed to the Navier-Stokes equations. A two-dimensional computational code MVFT(multi-viscosity-fluid and turbulence) was developed for computing the multi-viscosity-fluids and the turbulent induced by the fluid interface instability. By applying the developed MVFT code,numerical computations were conducted by the Smagorinsky and Vreman subgrid eddy viscosity models,respectively to simulate the Richtmyer-Meshkov instability experiment of a shock-accelerated heavy gas cylinder in LANL. The heavy gas column shapes,the flow field velocities and the vortex properties were analyzed and compared with the existent experimental and calculated results. It is indicated that the Vreman subgrid eddy viscosity model is superior to the Smagorinsky's in this simulation. The developed MVFT method and code are suitable for simulating the interface instability and turbulence mixing complex process.