Abstract:

Low-dissipation and low-dispersion high-order compact finite difference schemes are studied for computation of wave motion. An optimized seven-point sixth order accurate compact finite difference scheme (CO6) is obtained to approximate spatial derivatives, and is compared with the C6 (sixthorder compact) and C8 (eighth-order compact) schemes. For time marching scheme, the fourth order explicit Runge-Kutta methods (RK4 and LDDRK or RK46) are used. The effective wave-number ranges of the spatial schemes, the numerical errors of the various schemes, and the minimum point numbers per wavelength (ppw) for long distance propagation calculation of waves are studied. Based on the comparison, suggestions are given in using these schemes. Finally, a few numerical tests are presented to show accuracy of the schemes in simulation of wave motion.