Application of a shock-fitted spectral collocation method for computing transient high-speed inviscid flows over a blunt nose

Interaction of freestream disturbances with high-speed inviscid flow over a blunt nose is simulated utilizing a shock-fitted spectral collocation method. The unsteady flow computations are made through solving the 2D Euler equations by virtue of such a dissipation-free numerical algorithm for precise unsteady flow simulations. A shock-fitting technique is employed to accurately compute the unsteady shock motions and its interaction with monochromatic freestream disturbances of different conditions. A symmetry condition is proposed to accurately model the both steady and unsteady characters of the symmetry boundary, which allows the use of halved geometries and avoids the extra computational cost. The computational results for a cylinder at Mach 8.03 are presented and verified through comparisons with other numerical and promising analytical solutions. The stagnation line where the most energetic interactions take place is inspected carefully. The study shows the significant influence of the shock on its subsequent flow field in unsteady simulations and notable ability of the shock-fitted spectral collocation method implemented for the study of such problems.