Analysis of Numerically Induced Oscillations in Two-Dimensional Finite-Element Shallow-Water Models Part II: Free Planetary Waves
Analysis of Numerically Induced Oscillations in Two-Dimensional Finite-Element Shallow-Water Models Part II: Free Planetary Waves
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二维有限元浅水模型中的数值诱发振荡分析第二部分：自由行星波
DOI：
10.1137/070697872
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
B. Pouliot
中科院分区：
文献类型：
--
作者：
D. Y. Roux;B. Pouliot
通过使用中纬度 $\beta$ 平面二维线性浅水方程的准地转近似，研究了有限元数值模型中行星（罗斯比）波的行为。这里采用色散关系分析来确定可能出现的寄生模式并确定有限元伽辽金混合公式的色散/耗散性质。通过使用各种混合插值方案来考虑三个有限元对。对于每一对，获得并分析频率或色散关系，并通过分析和图形方式将色散特性与连续情况进行比较。结果表明，由于动量方程和连续性方程之间的耦合，混合插值方案的某些选择可能会导致慢罗斯贝波计算中出现显着的相位和群速度误差以及虚假解。模拟慢罗斯贝波的两个试验问题的数值解与解析结果非常吻合。
The behavior of planetary (Rossby) waves in finite-element numerical models is investigated by using a quasi-geostrophic approximation to the midlatitude, $\beta$-plane, two-dimensional linear shallow-water equations. A dispersion relation analysis is employed here to determine the possible occurrence of spurious modes and to ascertain the dispersive/dissipative nature of the finite-element Galerkin mixed formulation. Three finite-element pairs are considered by using a variety of mixed interpolation schemes. For each pair the frequency or dispersion relation is obtained and analyzed, and the dispersion properties are compared analytically and graphically with the continuous case. It is shown that certain choices of mixed interpolation schemes may lead to significant phase and group velocity errors and spurious solutions in the calculation of slow Rossby waves, due to the coupling between the momentum and continuity equations. Numerical solutions of two test problems to simulate slow Rossby waves are in good agreement with the analytical results.