A Hybrid Numerical Simulation of Supersonic Isotropic Turbulence (Communications in Computational Physics, 2018)
This paper presents an extension work of the hybrid scheme proposed byWang et al. [J. Comput. Phys. 229 (2010) 169-180] for numerical simulation of subsonicisotropic turbulence to supersonic turbulence regime. The scheme still utilizesan 8th-order compact scheme with built-in hyperviscosity for smooth regions and a7th-order WENO scheme for highly compression regions, but now both in their conservationformulations and for the latter with the Roe type characteristic-wise reconstruction.To enhance the robustness of the WENO scheme without compromisingits high-resolution and accuracy, the recursive-order-reduction procedure is adopted,where a new type of reconstruction-failure-detection criterion is constructed from theidea 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 butalso extends largely the computable range of turbulent Mach number, which has beenfurther confirmed by numerical results.
Keywords: Supersonic turbulence; hybrid scheme; positivity-preserving ROR-WENO scheme; compact scheme.