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1. 北京航空航天大学 航空科学与工程学院, 北京 100083;
2. 中国兵器工业导航与控制技术研究所, 北京 100190

An improved interpolation method for hybrid overset grid and its application
HUANG Yu1, YAN Chao1, WANG Wen1, XI Ke2
1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
2. Institute of Ordnance Industry Navigation and Control Technology, Beijing 100190, China
Received: 2016-01-29; Accepted: 2016-04-29; Published online: 2016-06-30 09:04
Corresponding author. YAN Chao,E-mail:yanchao@buaa.edu.cn
Abstract: For overset grid, reasonable interpolation between grids is one of the bases to ensure correct calculation of flow fields. In this paper, a new interpolation method for hybrid overset grid is presented, which focuses on the elimination of interpolation error coming from the grids mismatch at the intergrid boundary. With the combination of second order accuracy interpolation and proper selection and expansion of interpolation template by grid size, the interpolating accuracy of the cases with poor overset grids matching is improved. The presented method is suitable for arbitrary polyhedral grid and easy to be implemented. Compared with original method, numerical tests show that the presented method interpolates flow field variables with less dissipation when bad grids matching happened at the intergrid boundary, the variable contour at the intergrid boundary is smoother, and computational results agree more with the experimental data.
Key words: computational fluid dynamics     hybrid grid     overset grid     interpolation method     interpolation accuracy

1 原插值方法

 (1)

 图 1 重叠区域网格尺寸不匹配 Fig. 1 Mismatch of grid scale at overset area
2 混合重叠网格插值方法的改进

2.1 二阶精度的插值方法

 (2)

 (3)

 图 2 二阶插值示意图 Fig. 2 Illustration of 2nd order interpolation
 (4)

 (5)

 (6)

 (7)

 (8)

2.2 插值单元同宿主单元的关系分类

 图 3 3类插值单元和宿主单元重叠情况示意图 Fig. 3 Three types of relationship of interpolation and donor cells at overset area

2.3 流动变量插值策略

2.3.1 第2类情况策略

1) 扩展插值模板。采用Frink[14]加权重构方法，利用宿主相邻单元的格心值进行线性距离导数加权插值，在宿主网格上(见图 4(a)中网格1)，将宿主单元附近的正常单元格心变量插值到宿主单元的格点上，如图 4(a)所示。加权公式为

 图 4 第2类情况插值示意图 Fig. 4 Illustration of second interpolation type
 (9)

2) 利用宿主单元(见图 4(b)中网格1)上格点变量，依次对插值网格(见图 4(b)中网格2)单元中心采用式(2)、式(5)和式(6)进行二阶精度插值，获得插值单元格心处变量。

2.3.2 第3类情况策略

 图 5 第3类情况插值示意图 Fig. 5 Illustration of third interpolation type

2.4 梯度和限制器函数的计算

 (10)

3 控制方程及数值方法

 (11)

4 算例及计算结果

4.1 RAE2822超临界翼型

 图 6 RAE2822翼型重叠网格 Fig. 6 Overset grid of RAE2822 wing figure

 图 7 2种插值方法的马赫数分布比较 Fig. 7 Mach number contour distribution comparison of two interpolation methods
 图 8 翼面压力系数分布 Fig. 8 Pressure coefficient distribution on wing surface

 图 9 2种插值方法的尾涡无量纲涡黏性分布对比 Fig. 9 Rear eddy nondimensional viscosity contour distribution comparison of two interpolation methods

 图 10 2种插值方法的残差收敛情况对比 Fig. 10 Comparison of residual error convergence history of two interpolation methods
4.2 三维机翼抛弹分离

 图 11 三维机翼挂架重叠网格 Fig. 11 3D overset grid of wing/pylon/store

 图 12 0.3 s时刻对称面和物面压力分布 Fig. 12 Surface and symmetry pressure contour at 0.3 s
 图 13 初始时刻5°和185°子母线压力系数分布 Fig. 13 Pressure coefficient distribution on circumferential location 5° and 185° at initial time
 图 14 外挂物质心和姿态角随时间变化 Fig. 14 Variation of store movement and attitude angle with time
5 结 论

1) 本文插值策略适用于各种类型网格单元，且对各类单元处理过程类似，能保证混合重叠网格计算中流场变量传递的合理性和正确性。

2) 引入二阶精度插值方法，降低了重叠区插值引起的误差，在插值区网格尺寸匹配度较差时，流场变量经过插值区后保持得更好，耗散更低。

3) 进行插值误差修正时，直接使用当前时间步获得的梯度计算中获得了加权节点值，减小了额外计算量。

4) 本文插值策略根据插值区网格尺寸匹配度情况选择不同的方法，仅对尺寸匹配度较差时采用本文方法，可以有效地减低插值计算的时间，并对二维和三维情况均有较好的适用性。

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#### 文章信息

HUANG Yu, YAN Chao, WANG Wen, XI Ke

An improved interpolation method for hybrid overset grid and its application

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(2): 285-292
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0114