Optimized composite finite difference schemes for atmospheric flow modeling
Optimized composite finite difference schemes for atmospheric flow modeling
复制标题
大气流动建模的优化复合有限差分格式
DOI：
10.1002/num.22407
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发表时间：
2019
影响因子：
3.9
通讯作者：
A. Appadu
中科院分区：
文献类型：
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作者：
A. Appadu
在本文中，我们使用一些有限差分方法来解决由平流扩散方程描述的大气流动问题。 Clancy 使用前向时间中心空间 (FTCS) 方案解决了该流动问题，由于相位和幅度误差较大，尤其是在长传播时间下产生的误差，因此模拟具有挑战性。 Clancy 还导出了 FTCS 方案的稳定性极限。我们使用冯·诺依曼稳定性分析和 Hindmarsch 等人的方法。这是对 Clancy 技术的改进技术，旨在获得 FTCS、Lax-Wendroff (LW)、Crank-Nicolson 等某些方法的稳定区域。我们还构建了一个非标准有限差分（NSFD）方案。研究了稳定性和一致性等特性。为了改善由于显着的数值色散或数值耗散而导致的结果，我们得出了一种新的复合方案，该方案由三个 LW 应用程序和一个 NSFD 应用程序组成。后者就像一个滤波器，可以消除 LW 中的色散振荡。我们通过使用两种技术计算给定空间步长下的最佳时间步长来进一步改进复合方案：通过最小化色散误差的平方以及最小化色散和耗散误差的平方和。
In this paper, we use some finite difference methods in order to solve an atmospheric flow problem described by an advection–diffusion equation. This flow problem was solved by Clancy using forward‐time central space (FTCS) scheme and is challenging to simulate due to large errors in phase and amplitude which are generated especially over long propagation times. Clancy also derived stability limits for FTCS scheme. We use Von Neumann stability analysis and the approach of Hindmarsch et al. which is an improved technique over that of Clancy in order to obtain the region of stability of some methods such as FTCS, Lax–Wendroff (LW), Crank–Nicolson. We also construct a nonstandard finite difference (NSFD) scheme. Properties like stability and consistency are studied. To improve the results due to significant numerical dispersion or numerical dissipation, we derive a new composite scheme consisting of three applications of LW followed by one application of NSFD. The latter acts like a filter to remove the dispersive oscillations from LW. We further improve the composite scheme by computing the optimal temporal step size at a given spatial step size using two techniques namely; by minimizing the square of dispersion error and by minimizing the sum of squares of dispersion and dissipation errors.