Numerical simulations of shock/obstacle interactions using an improved ghost-cell immersed boundary method

•A ghost-cell immersed boundary method with improved accuracy is proposed.•The shock propagation at high Mach number is greatly influenced by the boundary layer.•Evolution of shock/boundary layer interactions is divided into three stages.•Worm-like structure and shock bifurcation indicate a certain kind of instability. An improved ghost-cell immersed boundary method coupled with a high-order finite difference scheme is currently proposed to numerically simulate the reflected shock/boundary layer interaction in a wavy-wall tube. The main improvement of current algorithm involves the particular treatment of the solid boundary reconstruction procedure by using both ghost points in solid domain and forcing points in fluid domain together. Owing to this kind of improvement operation, the amount of points used to recover the solid boundary increases greatly and will inevitably promote the accuracy of solid boundary reconstruction, which will play a significant role in the current high-order accurate numerical simulation. A typical validation case of 2-dimensional shock/circular cylinder interaction is conducted and demonstrate that the current improved numerical method can be used to capture the flow details such as shock bifurcation and small vortex very well and improve the numerical precision greatly. The improved method is then applied to numerically investigate the effects of boundary layer on the propagation of the shock in a wavy-wall tube. It is observed that, at low Mach number, the existence of boundary layer has little effect on the shock propagation. As the Mach number increases to 1.9, some certain complicated flow features will occur due to the enhanced boundary layer effects. In the early stage, the flow structures are nearly the same as those without the boundary layers. In the transition stage, a high-speed shear band behind the leading shock is observed and finally evolves into a worm-like structure, whose instability is illustrated by qualitative assessment on its flow features. In the developing stage, a remarkable shock bifurcation phenomenon is present and the worm-like structures will start shedding regularly, which will induce a series of scattering-like waves and asymmetrical flow fields. These characteristics demonstrate that the bifurcated shock waves located in upper and lower walls of the wavy-wall shock tube act as a primary trigger to gradually destabilize the shocked flow.