Wave dispersion properties of compound finite elements
Wave dispersion properties of compound finite elements
复制标题
复合有限元的波色散特性
DOI：
10.1016/j.jcp.2017.02.025
复制
发表时间：
2017
影响因子：
4.1
通讯作者：
Melvin T
中科院分区：
文献类型：
--
作者：
Melvin T
混合有限元对不同的因变量使用不同的逼近空间。某些类别的混合有限元，称为兼容有限元，已被证明表现出一些理想的属性的数值天气预报模式。在二维中，基于Raviart-Thomas的混合单元的最低阶单元是广泛使用的C-网格交错的有限元等效物，已知C-网格交错具有良好的波频散特性，至少对于四边形网格。最近有人提出，从许多三角形Raviart-Thomas子元素构建复合元素，使得原始和（隐含的）对偶网格都是从相同的子元素构建的，这将允许在使用不同的平流方案时具有更大的灵活性，沿着构建任意多边形元素的能力。虽然三角形子单元的波色散特性是很好的理解，那些复合元素是未知的。了解它们与非复合单元的比较情况以及三角形子网格单元继承了哪些特性将是有用的。在这里提出了一个数值色散分析的线性浅水方程在二维离散使用最低阶复合Raviart-Thomas有限元规则四边形和六边形网格。结果发现，与众所周知的C-网格方案相比，复合元素表现出更各向同性的色散关系，与相对较大的低估相比，短波的频率有一个小的高估C-网格。在一个四边形网格上的复合元素被发现不同于非复合Raviart-Thomas四边形元素，即使是均匀的元素，表现出的影响，基本的子元素。这表明，导致小的改善的色散关系的精度：复合四边形元素是稍微好一点的重力波，但略差的惯性波比标准的最低阶Raviart-Thomas元素。
Mixed finite elements use different approximation spaces for different dependent variables. Certain classes of mixed finite elements, called compatible finite elements, have been shown to exhibit a number of desirable properties for a numerical weather prediction model. In two-dimensions the lowest order element of the Raviart–Thomas based mixed element is the finite element equivalent of the widely used C-grid staggering, which is known to possess good wave dispersion properties, at least for quadrilateral grids. It has recently been proposed that building compound elements from a number of triangular Raviart–Thomas sub-elements, such that both the primal and (implied) dual grid are constructed from the same sub-elements, would allow greater flexibility in the use of different advection schemes along with the ability to build arbitrary polygonal elements. Although the wave dispersion properties of the triangular sub-elements are well understood, those of the compound elements are unknown. It would be useful to know how they compare with the non-compound elements and what properties of the triangular sub-grid elements are inherited?Here a numerical dispersion analysis is presented for the linear shallow water equations in two dimensions discretised using the lowest order compound Raviart–Thomas finite elements on regular quadrilateral and hexagonal grids. It is found that, in comparison with the well known C-grid scheme, the compound elements exhibit a more isotropic dispersion relation, with a small over estimation of the frequency for short waves compared with the relatively large underestimation for the C-grid. On a quadrilateral grid the compound elements are found to differ from the non-compound Raviart–Thomas quadrilateral elements even for uniform elements, exhibiting the influence of the underlying sub-elements. This is shown to lead to small improvements in the accuracy of the dispersion relation: the compound quadrilateral element is slightly better for gravity waves but slightly worse for inertial waves than the standard lowest order Raviart–Thomas element.
登录
查看更多内容
影响因子：
2.3
作者：
S. Danilov
通讯作者：
S. Danilov
影响因子：
4.1
作者：
D. Y. Roux
通讯作者：
D. Y. Roux
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
发表时间：
2008
期刊：
SIAM J. Sci. Comput.
影响因子：
--
作者：
D. Y. Roux;B. Pouliot
通讯作者：
B. Pouliot
DOI：
10.1142/s021820250800284x
发表时间：
2008-05-01
影响因子：
3.5
作者：
Christiansen, Snorre H.
通讯作者：
Christiansen, Snorre H.
影响因子：
8.9
作者：
A. Staniforth;T. Melvin;C. Cotter
通讯作者：
A. Staniforth;T. Melvin;C. Cotter