Convergence Tests for the Piecewise Parabolic Method and Navier–Stokes Solutions for Homogeneous Compressible Turbulence

The need to simulate fully developed turbulence with wide range of scales led us to use the Piecewise Parabolic Method (PPM) to solve the Euler equations of motions. To obtain data for 3-D homogeneous compressible decaying turbulence numerical simulations were performed on computational meshes of up to 10243 zones. These data were compared with data obtained by solving the Navier–Stokes (NS) equations. Results of studying the kinetic energy, enstrophy, and the energy power spectra with different resolutions are presented for both the PPM and NS data. The results of the comparison show convergence of the PPM and NS solutions to the same limit.