Higher-order numerical simulation of unsteady shock/vortex interactions

An efficient numerical method for simulating unsteady shock/vortex interactions is proposed. The principal concept of the present method is to employ the fourth-order compact MUSCL TVD (PCMT) scheme proposed by the authors in space difference and a maximum second-order integral scheme in time integration. The combination of the higher-order numerical schemes enable us to capture shocks and contact surfaces accurately without numerical oscillations and to demonstrate the behavior of vortices interacting with shocks more clearly than most of the existing numerical solver. Also as additional distinctive advantage, the numerical schemes are constructed of quite simple algorithms. Especially by applying the FCMT scheme, existing solvers based on the MUSCL approach can be easily extended to a higher-order one. Finally, transonic viscous flows around a circular cylinder, which is known as a typical flow problem accompanied by unsteady shock/vortex interactions, are calculated and visualized, and the unsteady shock/vortex structure is numerically investigated.