High-Order Optimized Numerical Schemes for Computational Aeroacoustics

This paper presents a new optimization approach for the high-order finite difference schemes. Due to the fact that it is common for a sound field to consist of several dominant wavenumbers, the proposed numerical schemes are optimized at these dominant wavenumbers instead of over a range of wavenumber. These optimized multi-component schemes, as referred to in this paper, give very accurate solutions if used to predict an acoustic wave traveling with these dominant wavenumbers. In addition, for broadband waves, it is shown that the performance of the optimized upwind multi-component scheme is comparable to that of the optimized upwind broadband scheme, which is optimized over a range of wavenumber. The results of the Fourier analysis also show that the optimized central multi-component schemes are at least comparable to if not better than the optimized central broadband schemes when solving broadband waves.