When the classic compact finite difference scheme was applied to practical problems using non-uniform meshes

the spurious numerical oscillations would be excited.A high accuracy of compact scheme was developed for this problem.The general expressions of the scheme's coefficients were derived through Taylor expansion analysis;then the numerical dispersion and dissipation were analyzed by using Fourier analysis method.For the case that the sixth-order tridiagonal compact scheme was applied to non-uniform meshes

the results are shown:the dispersion and dissipation values are closer to the exact solution with the increase of disturbance factor;the scheme is asymptotically stable when the disturbance factor is less than or equal to 0.213

otherwise it is the opposite;the results of numerical solution for one-dimensional convective wave and two-dimensional wave propagation agree well with the theoretical solution

which shows advantages in the simulation of non-uniform meshes for computational aeroacoustis.