Parametric study of WENO schemes in truncation, dissipation, and dispersion errors

Based on the dissipation and dispersion relations, eight weighted essentially non-oscillatory (WENO) schemes are investigated for computational aeroacoustics. For demand of high-order accuracy, all of WENO schemes are asked to be at least fourth-order accurate. Therefore, with a reasonable number of grid points, they can simulate the low-frequency waves in high order accuracy. But, for the higher frequency waves, two parameters in the WENO schemes are introduced to determine which scheme is better on the dissipation and dispersion errors. Both upwind and central schemes are considered and compared by the order of accuracy and the capability of wave capturing. A sequence of numerical simulations was 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.