﻿ 非结构重叠网格显式装配算法<sup>*</sup>
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Explicit assembly algorithm of unstructured overset grid
XUAN Chuanwei, HAN Jinglong
State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Received: 2019-01-17; Accepted: 2019-04-05; Published online: 2019-04-30 16:02
Foundation item: National Natural Science Foundation of China (11472133); the Priority Academic Program Development of Jiangsu Higher Education Institutions
Corresponding author. HAN Jinglong, E-mail: hjlae@nuaa.edu.cn
Abstract: To solve the problem that the hole mapping method occupies too much physical memory, an improved hole mapping method was developed. Based on the neighbor-to-neighbor search algorithm, a donor search method based on adjacent front was developed. An explicit assembly algorithm of unstructured overset grid was presented by combining the cut-paste method with the implicit cutting technique. First, the algorithm generated a set of Cartesian grids surrounding the wall surface. Second, those Cartesian cells intersecting the wall surface were stored. Finally, relative positions of the stored Cartesian cells were used to determine whether a grid point was inside the wall. After successfully determining all the grid points inside the wall, the current fringe grid points were used as the initial front, and the overlapping area was optimized by the wall distance of each grid point to generate the final interpolation boundary. The proposed explicit algorithm optimizes the traditional implicit assembly process of unstructured overset grid. It features in low physical memory occupation, low cost of donor searching and high computational efficiency. The accuracy and applicability of the proposed explicit method were verified by two typical complex flow examples.
Keywords: overset grid     cut-paste method     hole mapping     unstructured grid     wall distance

1 洞映射法及其改进 1.1 传统洞映射法

 (1)

1.2 改进型洞映射法

 图 1 改进型洞映射法产生的笛卡儿网格示意图 Fig. 1 Cartesian grids of improved hole mapping method

2 显式网格装配算法 2.1 割补法

2.2 基于相邻阵面的贡献单元搜索技术

 图 2 基于阵面推进的相邻单元搜索法 Fig. 2 Neighbor-to-neighbor search algorithm based on advancing front

1) 在初始挖洞结束之后，建立2个空链表LI和LJ，将所有当前洞边界点(I0I1，…，In)推入链表LI。

2) 查找链表LI中首节点I0的贡献单元D0

3) 以D0为起始单元通过相邻单元搜索法查找I1的贡献单元D1，再以D1为起始单元搜索I2的贡献单元D2，如此推进直至遍历链表LI中所有节点并对所有已搜索过贡献单元的节点进行标记。

4) 清空链表LJ，遍历链表LI，查询每个节点Ii的相邻节点Ji，若Ji未被标记则以Ii的贡献单元Di为起始单元通过相邻单元搜索法搜索节点Ji的贡献单元，然后将其推入链表LJ。

5) 清空LI，将LJ中所有节点推入LI，重复步骤4)，如此通过2个链表互相迭代推进洞边界位置。

2.3 网格装配算法

1) 循环所有网格，计算各网格单元到物面的距离并将所有单元标记为正常单元。

2) 采用本文改进型洞映射法挖去所有洞内单元，将位于物面内部的网格单元标记为洞内单元，与洞内单元相邻的正常单元标记为洞边界单元。

3) 以上述洞边界单元为初始阵面推进，并以本文所发展的基于相邻阵面的贡献单元搜索法搜索并保存其贡献单元信息。在阵面推进过程中，比较该洞边界单元与其贡献单元的物面距大小。若前者大于后者，则将该洞边界单元标记为洞内单元，而与其相邻的正常单元标记为洞边界单元。当洞边界单元的物面距小于或等于其贡献单元的物面距时结束该过程。

4) 为保证二阶计算精度，将与洞边界单元相邻的2个洞内单元标记为插值单元，同时将该洞边界单元标记为正常单元。

 图 3 非结构重叠网格显式装配技术 Fig. 3 Explicit assembly technique of unstructured overset grid

 算法 贡献单元搜索次数 时间/s 本文算法 4 134 1.25 传统隐式算法 38 815 5.12

3 算例 3.1 计算方法

3.2 30P30N三段式机翼

 图 4 30P30N机翼重叠网格图 Fig. 4 Overset mesh of 30P30N wing
 图 5 30P30N翼面马赫数云图 Fig. 5 Mach number contour of 30P30N wing surface
 图 6 30P30N翼面压力系数的数值与试验结果对比 Fig. 6 Comparison of pressure coefficient of 30P30N wing surface between numerical and experimental results
3.3 Titan Ⅳ运载火箭

 图 7 Titan Ⅳ非结构重叠网格系统 Fig. 7 Unstructured overset mesh system for Titan Ⅳ
 图 8 Titan Ⅳ对称面重叠网格 Fig. 8 Overset mesh of Titan Ⅳ's symmetry plane
 图 9 Titan Ⅳ对称面压力云图 Fig. 9 Pressure contour of Titan Ⅳ symmetry plane
 图 10 芯级中心线压力分布 Fig. 10 Pressure distribution along rocket center line

 性能指标 算法 30P30N Titan Ⅳ 内存占用/MB 本文算法 77.66 1 023.77 传统洞映射 151.23 1 903.58 贡献单元搜索时间/s 本文算法 2.12 29.50 传统隐式算法 10.35 126.43

4 结论

1) 通过对传统洞映射过程进行优化，发展了一种改进型洞映射法，并大大减少了洞映射过程中对计算机内存空间的占用。

2) 结合割补法与相邻单元搜索法的特点，发展了一种基于相邻阵面的贡献单元搜索法，优化了贡献单元搜索过程，提高了搜索效率。

3) 与传统非结构重叠网格隐式装配过程相比，本文所提显式装配过程具有更高的效率。

4) 通过30P30N三段式机翼和Titan Ⅳ运载火箭2个经典算例验证了本文算法的准确性与可靠性。

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#### 文章信息

XUAN Chuanwei, HAN Jinglong

Explicit assembly algorithm of unstructured overset grid

Journal of Beijing University of Aeronautics and Astronsutics, 2019, 45(10): 2026-2034
http://dx.doi.org/10.13700/j.bh.1001-5965.2019.0020