Figure 5

Energy spectra (equation ( 10 )) obtained with different numerical methods and resolutions. The energy spectra are compensated by a \(k^{5/3}\) spectrum, so that any region with Kolmogorov scaling should appear roughly flat. Furthermore, the spectra are all plotted as a function of the dimensionless wave number \(512 k \Delta x\) (the 512 factor is introduced to have the dimensionless wave number coincide with the dimensional one for the 512³ runs). The first five panels show the PPM_HLLC (upper left), PPM_HLLC_CFL0.8 (upper center), PPM_HLLE (upper right), TVD_HLLE (lower left) and WENOZ_HLLC (lower center) group of runs. The last panel (lower right) shows a comparison of all of the methods at the highest resolution (512³). An inertial range seems to be recovered only at the highest resolutions (perhaps with the exception of TVD_HLLE where no inertial range is visible). All schemes employing the HLLC Riemann solver are in very good agreement.