Mass Residuals as a Criterion for Mesh Refinement in Continuous Galerkin Shallow Water Models
Mass Residuals as a Criterion for Mesh Refinement in Continuous Galerkin Shallow Water Models
复制标题
质量残差作为连续 Galerkin 浅水模型网格细化的准则
DOI：
10.1061/(asce)0733-9429(2008)134:5(520
复制
发表时间：
2008
影响因子：
2.4
通讯作者：
K. Dresback
中科院分区：
文献类型：
--
作者：
J. Dietrich;R. Kolar;K. Dresback
传统上计算质量平衡误差的方法是利用质量守恒方程的传统通量，但最近的文献支持一种基于通量的方法，该方法与控制方程的离散化是一致的。通过将这两种方法的质量残差与控制方程离散化产生的截断误差进行比较，我们发现传统的通量产生的质量残差更能描述模型的整体行为，即它们与截断误差有更好的相关性。然后，我们证明了这些质量残差可以作为网格细化的标准。在一个使用一维浅水模型的例子中，我们证明了通过将节点从质量残差较大的区域移动到质量残差较小的区域，可以得到比使用局部截断误差分析得到的网格具有更小的截断误差的网格。并以一个二维浅水模型为例，证明了在质量残差较大的区域，可以通过网格加密来改进计算结果。
Mass balance error has been computed traditionally by using conventional fluxes derived from the conservation of mass equation, but recent literature supports a method based on fluxes that are consistent with the discretization of the governing equations. By comparing the mass residuals from these two methods to the truncation errors produced by the discretization of the governing equations, we show that the conventional fluxes produce mass residuals that are more descriptive of the overall behavior of the model, i.e., they are better correlated with truncation error. Then we demonstrate that these mass residuals can be used as a criterion for mesh refinement. In an example using a one-dimensional shallow water model, we demonstrate that, by moving nodes from regions with large mass residuals to regions with small mass residuals, a mesh can be developed that shows less truncation error than a mesh developed by using localized truncation error analysis. And, in an example using a two-dimensional shallow water model, we demonstrate that the computed solution can be improved in regions with large mass residuals through mesh refinement.