Analysis of the Effects of Numerical Dispersion on Pulses in Finite-difference and Pseudospectral Time-domain Methods

Abstract

Finite difference (FD) and pseudospectral (PS) time‐domain methods are increasingly used forunderwater acoustics modeling. Numerical dispersion is unavoidable but can be reduced with an appropriate choice of temporal and spatial discretization (Δt and Δx). As pulses propagate, numerical dispersion causes time‐dilation which increases with simulation time and pulse bandwidth. Analysis of the dispersion relation leads to an equation which shows that the time‐dilation in a large FD model can be significant for well defined pulses of 50 points per wavelength (PPW). Reducing the dispersion requires a higher grid density. For a 2D model, the memory requirement and time costs vary as the inverse square and inverse cube of Δx. This is contrasted with the PS model in which the time‐dilation can be set arbitrarily small for any choice of Δx by reducing Δt. For a fixed spatial grid density, e.g., 10 PPW, the computational cost is linear in the temporal grid density. A locally optimized short‐time fractional Fourier transformshows that numerical dispersion has a dramatic effect on the time‐frequency characteristics of dispersed pulses, e.g., an input CW pulse becomes a nonlinear upward chirp. These effects are illustrated for a variety of pulses.

Department

Center for Coastal and Ocean Mapping

Publication Date

11-2001

Volume

110, Issue 5

Journal Title

Journal of the Acoustical Society of America

Pages

2618-2618

Publisher Place

Melville, NY, USA

Rights

© 2001 Acoustical Society of America

Publisher

Acoustical Society of America

Digital Object Identifier (DOI)

10.1121/1.4776815

Document Type

Journal Article

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