Numerical simulation of shocked sound waves using compact scheme

Numerical computations of time dependent Euler's equations of a quasi-one dimensional shock flow field in a convergent-divergent nozzle are performed. The time dependent nature of the flow field is initiated by a very small amplitude and high frequency acoustic wave superimposed on steady flow. Computations are performed using a three points sixth-order compact scheme to approximate the spatial derivatives and the low storage optimized 4-6 Low Dispersion and Dissipation Runge-Kutta (LDDRK) method as a time-marching scheme. To damp spurious high frequency waves generated in the numerical solution, we add artificial damping terms. For boundary treatment, radiation boundary conditions are used for subsonic inflow and the characteristic boundary conditions are used for subsonic outflow. The obtained numerical solutions with acoustic perturbation are presented.