Abstract: By using a splitting technique, the flux of the Navier Stokes governing equations including heat exchange and viscosity are divided into three parts, so called inviscid flux, viscous flux and heat flux, to calculate. The inviscid part of flux is evaluated using a high resolution multi-fluid parabolic piecewise method, the viscous part of flux is computed with a second order central difference in space and two-step Rung-Kutta scheme in time, and the heat flux part is not considered. Influences of fluid viscosity on instability of the interface between two fluids are revealed by computation results of the examples of Riemann problem in shock tube, two and three dimensional Richtmyer-Meshkov instabilities using the Navier Stokes governing equations and Euler governing equations.