Parametric study of weighted essentially nonoscillatory schemes for computational aeroacoustics

Based on the dissipation and dispersion relations, two groups of weighted essentially nonoscillatory (WENO) schemes are investigated for computational aeroacoustics, For high-order accuracy, all of the WENO schemes are required to be at least fourth-order accurate, Therefore, with a reasonable number of grid points, they can simulate the low-frequency waves with high-order accuracy. Also, for the higher frequency waves, two parameters in the WENO schemes are introduced to reduce their dissipation and dispersion errors. Both upwind and central schemes are considered and compared for order of accuracy and capability of wave capturing, A sequence of numerical simulations is carried out, These test problems are propagation of a sine-wave packet, propagation of a spherical wave, shock and sine wave interactions, and propagation of acoustic, vorticity, and density pulses in a freestream.