High-accuracy algorithms for computational aeroacoustics

This paper presents an analysis of high-bandwidth operators developed for use with an essentially nonoscillatory (ENO) method. The spatial operators of a sixth-order ENO code are modified to resolve waves with as few as 7 points per wavelength (PPW) by decreasing the formal order of the algorithm. Numerical and analytical solutions are compared for the model problems of plane-wave propagation and sound generation by an oscillating sphere. These problems involve linear propagation, wave steepening, and shock formation. An analysis of the PPW required for sufficient accuracy shows that low-order algorithms need an excessive number of grid points to produce acceptable solutions. In contrast, high-order codes provide good predictions on relatively coarse grids. The high-bandwidth operators produce only modest improvements over the original sixth-order operators for nonlinear problems in which wave steepening is significant ; however, they clearly outperform the original operators for long-distance linear propagation. Because the high-bandwidth operators have the same stencil as the original sixth-order operators, these gains are achieved with no additional computational work.