Abstract: The compressible multi-viscousity-fluid piecewiseparabolic method (MVPPM) is developed for Navier-Stokes equations based onthe Eulerian multi-fluid piecewise parabolic method (MFPPM), the secondorder space central difference method and two-stage Rung-Kutta time marchingmethod. Simultaneously, a common mathematical approach, operator splittingtechnique was applied to obtain the molecule dynamics viscosity and heatflux effects on flow field. With the application of MVPPM, a numerical caseof a two-dimensional shock wave tube experiment from Atomic WeaponsEstablishment (AWE) is investigated to show a good agreement with theexperimental results. Moreover, the interface instability and subsequentmixing model of implosion dynamics are simulated with MFPPM and MVPPM in thetwo-dimensional cylindrical symmetry case. The evolvement of the inner andouter interfaces, velocity history and the distribution of subsequent mixingin the central cavitations induced by Rayleigh-Taylor (RT) interfaceinstability are obtained. The effect of dynamics viscosity on the mixingdistribution in the interface was clearly observed in the numerical results.