NUMERICAL SIMULATIONS OF 3-DIMENSIONAL SUPERSONIC FLOWS

The Navier-Stokes equations are integrated numerically for three-dimensional homogeneous compressible decaying flows following the perfect-gas law for Reynolds numbers up to 120 and fluctuating Mach numbers between 1 and 4 initially. The code uses the collocation method, and has run with a grid of 128 uniformly distributed points. Many features, at that resolution, appear similar to the two-dimensional case. In particular: (i) at early times, where the flow is still supersonic, large scales are dominated by shear motions, and small scales by shocks, with as strong an inequipartition between the modes as in two dimensions. This effect will likely be alleviated but not totally erased for substantially higher Reynolds numbers; (ii) in the large time regime, a subsonic flow develops with dominance at all scales of the solenoidal mode. One further observes the marked appearance of regions of low density (0.1 or less of the mean value) presumably in the vicinity of strong shocks, with fluctuations in density that are quite large, a feature not present in the two-dimensional case at those Reynolds numbers. Finally it is found that the dissipation of kinetic energy is similar to the two-dimensional case in the supersonic regime but more intense in the subsonic regime.