Numerical simulation of transient hypersonic flow using the essentially nonoscillatory schemes

TLDR: In this paper, a numerical simulation of transient hypersonic flows involving shock-wave-freestream-disturbance interactions is presented using the essentially nonoscillatory (ENO) schemes.

Abstract: Numerical simulation of transient hypersonic flows involving shock-wave-freestream-disturbance interactions is presented using the essentially nonoscillatory (ENO) schemes. The ENO schemes were chosen for transient-flow simulations because they have high-order accuracy at extrema as well as in other parts of smooth solutions. First, the accuracy of the ENO schemes was tested numerically by applying them to the computations of a one-dimensional linear model equation and to an oscillating plate problem using the two-dimensional Navier-Stokes equations. Then, the third-order ENO scheme was used to compute the unsteady interaction of a freestream acoustic wave with a bow shock in hypersonic flow past a cylinder. The numerical results along the stagnation line were compared with linearized analytical solutions. The results show that the disturbance waves generated behind the bow shock are significantly amplified by the back-and-forth interactions and reflections of the acoustic waves. These results on the bow-shock-disturbance interactions will be useful in understanding the effects of the bow shock wave on the receptivity of hypersonic boundary layers to freestream disturbances.