Wang Yongxian, Tu Houwang, Liu Wei, Xiao Wenbin, Lan Qiang
College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China.
Entropy (Basel). 2021 Jun 2;23(6):705. doi: 10.3390/e23060705.
The normal mode model is important in computational atmospheric acoustics. It is often used to compute the atmospheric acoustic field under a time-independent single-frequency sound source. Its solution consists of a set of discrete modes radiating into the upper atmosphere, usually related to the continuous spectrum. In this article, we present two spectral methods, the Chebyshev-Tau and Chebyshev-Collocation methods, to solve for the atmospheric acoustic normal modes, and corresponding programs are developed. The two spectral methods successfully transform the problem of searching for the modal wavenumbers in the complex plane into a simple dense matrix eigenvalue problem by projecting the governing equation onto a set of orthogonal bases, which can be easily solved through linear algebra methods. After the eigenvalues and eigenvectors are obtained, the horizontal wavenumbers and their corresponding modes can be obtained with simple processing. Numerical experiments were examined for both downwind and upwind conditions to verify the effectiveness of the methods. The running time data indicated that both spectral methods proposed in this article are faster than the Legendre-Galerkin spectral method proposed previously.
简正模模型在计算大气声学中很重要。它常被用于计算在与时间无关的单频声源下的大气声场。其解由一组向上层大气辐射的离散模式组成，通常与连续谱相关。在本文中，我们提出了两种谱方法，即切比雪夫 - 陶（Chebyshev - Tau）方法和切比雪夫 - 配置（Chebyshev - Collocation）方法，用于求解大气声学简正模，并开发了相应的程序。这两种谱方法通过将控制方程投影到一组正交基上，成功地将在复平面中寻找模式波数的问题转化为一个简单的密集矩阵特征值问题，该问题可以通过线性代数方法轻松求解。在获得特征值和特征向量后，通过简单处理即可得到水平波数及其相应的模式。针对顺风和逆风条件进行了数值实验，以验证这些方法的有效性。运行时间数据表明，本文提出的两种谱方法都比先前提出的勒让德 - 伽辽金（Legendre - Galerkin）谱方法更快。
