A class of high order compact schemes with good spectral resolution for aeroacoustics

Abstract

In this paper, we design a class of linear compact schemes based on the cell-centered compact scheme of ((Lele, J Comput Phys 103:16–42, 1992). These schemes equate a weighted sum of the nodal derivatives of a smooth function to a weighted sum of the function on both the grid points and the cell-centers. Through systematic Fourier analysis and numerical tests, we observe that the schemes have good properties of high order, high resolution, and low dissipation. It is an ideal class of schemes for the simulation of multiscale problems such as aeroacoustics and turbulence.