Iwatsu R., Tsuru H., Hirosawa K.

Compact finite difference (FD) schemes on unevenly spaced staggered grid points are applied to the computation of acoustic wave propagation. The order of accuracy of these compact schemes is fourth and sixth and in the limit of evenly spaced grid intervals, they are identical to the corresponding schemes on evenly spaced grid points. The boundary formulations are derived and their accuracy and influence on the stability are analyzed. In order to improve the resolution of the schemes, the coefficients are numerically determined to minimize the dispersion and dissipation errors associated with spatial discretization. In the time integration, multi-step second and third-order optimized schemes are derived for staggered half-node arrangement of pressure and fluid particle velocity in time direction. These time integration schemes are optimized over a range of angular frequency of interest to minimize the error in the effective angular frequency of the time integration schemes. In combination with spatially optimized compact schemes, the present numerical schemes exhibit substantially improved frequency and wave height preserving characteristics for benchmark problems as compared with the conventional widely used FDTD (finite difference in time domain) scheme. Computation on unevenly spaced grid points showed that the proposed schemes perform well even on meshes with randomly displaced grid points. In the previous theoretical and numerical investigations, FD schemes with good wave propagation properties are derived solely on even grid points or for idealized problems. In the present study, numerical schemes are proposed that enable practical computation of wave equation on uneven grid points for the acoustics in complex geometries.