An efficient Euler solver using high-order upwind schemes and unstructured adaptive quadrilateral mesh is developed to simulate unsteady shock wave dynamics. To improve the shock instability problem, the Roe's approximate Riemann solver is replaced by the HLLE scheme for spatial descritization. Quadrilateral grid adopted in the present schemes has advantage over triangular grid in extending one-dimensional Riemann solver to multi-dimensional TVD schemes through operator splitting, H-type grid refinement/coarsening strategy is used for the unstructured grid adapted to the flow.
After solving several shock wave reflection phenomena to verify the present method, we investigated the pulsatile resonant flow of Hartmann-Sprenger tube and votex-shock interaction problem. For the Hartmann-Sprenger tube flow, the jet screech mode is predicted numerically for the first time in the present study and the jet regurgitant mode is also simulated. The periods of both modes are in good agreement with the experiment. The cyclic flow feature of the Hartmann-Sprenger tube is explained through pressure/density contours and velocity vector plots. The initial states leading to the periodic flow have provided furthur understanding of the resonant flow. For the shock-vortex interaction problem, sqew-symmetric sonic waves centered around the vortex stricken by the shock wave are clearly detected. The time-dependent structure of sonic waves in the form of compression and rarefaction waves are explained in detail.
