  In the Part 1 of the present paper the performance of several different low
and high-order finite-volume methods were assessed by investigating how well
they can capture the turbulent spectra of a compressible flow where small
smooth turbulent structures interact with shocks and discontinuities. The
comparisons showed that a second-order Godunov method with PPM interpolation
provides results virtually the same as a fourth-order WENO scheme but at a
significant lower cost. However, it is shown that the PPM method fails to
provide an accurate representation in the high-frequency range of the spectra.
In the present paper we show that this specific issue comes from the
slope-limiting procedure and a novel hybrid PPM/WENO method is developed, which
has the ability to capture the turbulent spectra with the accuracy of a
formally high-order method, but at the cost of the second-order Godunov method.
Overall, it is shown that virtually the same physical solution can be obtained
much faster by refining a simulation with the second-order method and carefully
chosen numerical procedures, rather than running a coarse high-order
simulation.
