Low-dispersion finite difference methods for acoustic waves in a pipe

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Abstract
A new algorithm for computing one‐dimensional acoustic waves in a pipe is demonstrated by solving the acoustic equations as an initial‐boundary‐value problem. Conventional dissipation‐free second‐order finite difference methods suffer severe phase distortion for grids with less that about ten mesh points per wavelength. Using the signal generated by a piston in a duct as an example, transient acoustic computations are presented using a new compact three‐point algorithm which allows about 60% fewer mesh points per wave length. Both pulse and harmonic excitation are considered. Coupling of the acoustic signal with the pipe resonant modes are shown to generate a complex transient wave with rich harmonic content.

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