Orthogonal grid generation of an irregular region using a local polynomial collocation method
Orthogonal grid generation of an irregular region using a local polynomial collocation method
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DOI：
10.1016/j.jcp.2013.01.005
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发表时间：
2013-06
期刊：
影响因子：
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通讯作者：
Nan-Jing Wu;T. Tsay;Tun-Chi Yang;Hung-Yuan Chang
中科院分区：
文献类型：
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作者：
Nan-Jing Wu;T. Tsay;Tun-Chi Yang;Hung-Yuan Chang
在本研究中，通过使用局部多项式配置方法和移动最小二乘（MLS）方法求解坐标变换的控制方程，开发了二维正交网格生成模型。该方法的发展思路是在边界上同时满足控制方程和边界条件，因此比传统的配置方法更加鲁棒和准确。尽管用于求解坐标变换方程的方法是无网格的，但它并没有降低当前工作的价值，因为现代使用的大多数数值模型都是依赖于网格的，并且仍然强烈需要为这些模型提供服务的网格生成，特别是对于不规则域中的有限差分模型。在应用于网格生成问题之前，通过基准势流问题测试了本方法的性能。除了两个基本的网格生成问题之外，还解决了先前工作的瓶颈问题，即域中包含零度角点。最后将该模型应用于多连通域中的正交网格生成。通过检查生成结果的正交性来证明正确性。
In this study, a 2-D orthogonal grid generation model is developed by solving the governing equations of coordinate transformation with a local polynomial collocation method accompanied with the moving least squares (MLS) approach. This method was developed in a way that on the boundaries both the governing equation and boundary condition are satisfied, so it is more robust and accurate than conventional collocation methods. Though the method used to solve the coordinate transforming equations is meshless, it does not deteriorate the value of present work, because most numerical models in modern use are grid-dependent, and grid generation of service to these models is still strongly desired, particularly for finite difference models in irregular domains. Before applying to grid generation problems, the performance of present method is tested by a bench mark potential flow problem. Additional to two basic grid generation problems, a bottleneck problem of previous works, which contains zero-degree corners in the domain, is carried out. Finally, the model is applied to the orthogonal grid generation in a multi-connected domain. The correctness is testified by checking the orthogonality of the generated results.