  This paper presents an extension of the hybrid scheme proposed by Wang et al.
(J. Comput. Phys. 229 (2010) 169-180) for numerical simulation of compressible
isotropic turbulence to flows with higher turbulent Mach numbers. The scheme
still utilizes an 8th-order compact scheme with built-in hyperviscosity for
smooth regions and a 7th-order WENO scheme for highly compressive regions, but
now both in their conservation formulations and for the latter with the Roe
type characteristic-wise reconstruction. To enhance the robustness of the WENO
scheme without compromising its high-resolution and accuracy, the
recursive-order-reduction procedure is adopted, where a new type of
reconstruction-failure-detection criterion is constructed. To capture the
upwind direction properly in extreme conditions, the global Lax-Friedrichs
numerical flux is used. In addition, a new form of cooling function is
proposed, which is proved to be positivity-preserving. With these techniques,
the new scheme not only inherits the good properties of the original one but
also extends largely the computable range of turbulent Mach number, which has
been further confirmed by numerical results.
