Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics

The normal mode model is important in computational atmospheric acoustics. It often used to compute the acoustic field under a time-independent single-frequency sound source. Its solution consists of set discrete modes radiating into upper atmosphere, usually related continuous spectrum. In this article, we present two spectral methods, Chebyshev-Tau and Chebyshev-Collocation solve for modes, corresponding programs are developed. methods successfully transform problem searching modal wavenumbers complex plane simple dense matrix eigenvalue by projecting governing equation onto orthogonal bases, which can be easily solved through linear algebra methods. After eigenvalues eigenvectors obtained, horizontal their obtained with processing. Numerical experiments were examined both downwind upwind conditions verify effectiveness running time data indicated that proposed article faster than Legendre-Galerkin method previously.