High-Accuracy Finite-Difference Schemes for Linear Wave Propagation

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Abstract
Two high-accuracy finite-difference schemes for simulating long-range linear wave propagation are presented: a maximum-order scheme and an optimized scheme. The schemes combine a seven-point spatial operator and an explicit six-stage low-storage time-march method of Runge--Kutta type. The maximum-order scheme can accurately simulate the propagation of waves over distances greater than five hundred wavelengths with a grid resolution of less than twenty points per wavelength. The optimized scheme is found by minimizing the maximum phase and amplitude errors for waves which are resolved with at least ten points per wavelength, based on Fourier error analysis. It is intended for simulations in which waves travel under three hundred wavelengths. For such cases, good accuracy is obtained with roughly ten points per wavelength.