Abstract: On the basis of the multi-fluid volume-of-fraction method and piecewise parabolic method, a multi-viscosity-fluid piecewise parabolic method(MVPPM) was proposed and the corresponding computer code was developed to investigate the multi-viscous-fluid dynamic problems. To verify and validate the developed code, a shock tube experiment of hydrodynamic instability and flow mixing induced by reshock was simulated numerically. The numerical results are in agreement with the experimental results. The evolution of the fluid mixing zone under reshock reveals that the mixing growth rate has a close dependence on the spectra and amplitudes of the initial perturbation, and at the moment the reshock arrives at and interacts with the interface, the fluid mixing zone width decreases sharply, then increases quickly again. Comparison between viscous and inviscid results displays that the molecular dynamics viscosity affects weakly on the fluid mixing zone.