Abstract: In this study, a new fully-implicit finite-volume numerical algorithm is developed tosolve the time-dependent Navier-Stokes equations using NND finite difference scheme. Both inviscid and viscous fluxes across cell boundaries are treated implicitly. The present work emphasizesthe finite-volume approximation of the integral form of the conservation laws. The integral approach enhances both stability and accuracy of the algorithm. Nonequilibrium reacting hypersonicionizing air viscous flows over the reentry v...