High-order unstructured curved mesh generation using the Winslow equations
High-order unstructured curved mesh generation using the Winslow equations
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DOI：
10.1016/j.jcp.2015.11.020
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发表时间：
2016-02-15
影响因子：
4.1
通讯作者：
Persson, Per-Olof
中科院分区：
文献类型：
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作者：
Fortunato, Meire;Persson, Per-Olof
提出了一种基于经典温斯洛方程的高阶非结构曲面网格生成方法。我们从参考域中的初始直边网格开始，并将边界上的节点位置固定在真正的弯曲几何上。在区域的内部，我们解决了温斯洛方程使用一种新的连续Galerkin有限元离散。该公式似乎产生高质量的弯曲元件，其高度抗反转。此外，相应的非线性方程可以有效地解决使用皮卡德迭代，即使是高度拉伸的边界层网格。与先前提出的几种技术相比，例如基于弹性类比的优化和方法，这可以显着降低计算成本，同时产生类似质量的弯曲单元。我们展示了一些例子，在两个和三个空间维度，包括复杂的几何形状和拉伸边界层，并证明了高质量的生成网格和非线性求解器的性能。(C)2015 Elsevier Inc.保留所有权利。
We propose a method to generate high-order unstructured curved meshes using the classical Winslow equations. We start with an initial straight-sided mesh in a reference domain, and fix the position of the nodes on the boundary on the true curved geometry. In the interior of the domain, we solve the Winslow equations using a new continuous Galerkin finite element discretization. This formulation appears to produce high quality curved elements, which are highly resistant to inversion. In addition, the corresponding nonlinear equations can be solved efficiently using Picard iterations, even for highly stretched boundary layer meshes. Compared to several previously proposed techniques, such as optimization and approaches based on elasticity analogies, this can significantly reduce the computational cost while producing curved elements of similar quality. We show a number of examples in both two and three space dimensions, including complex geometries and stretched boundary layers, and demonstrate the high quality of the generated meshes and the performance of the nonlinear solver. (C) 2015 Elsevier Inc. Allrightsreserved.