(untitled) (Communications in Computational Physics, 2018)
This paper presents an extension work of the hybrid scheme proposed by Wang et al. [J. Comput. Phys. 229 (2010) 169-180] for numerical simulation of subsonic isotropic turbulence to supersonic turbulence regime. The scheme still utilizes an 8th-order compact scheme with built-in hyperviscosity for smooth regions and a 7th-order WENO scheme for highly compression 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 from the idea of positivity-preserving. In addition, a new form of cooling function is proposed, which is proved also to be positivity-preserving. With a combination of 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.