基于单元相交的混合网格精确守恒插值方法

徐春光; 董海波; 刘君

doi:10.11883/1001-1455(2016)03-0305-08

基于单元相交的混合网格精确守恒插值方法

doi: 10.11883/1001-1455(2016)03-0305-08

大连理工大学航空航天学院，辽宁大连 116024

基金项目:

国家自然科学基金项目 11272074

辽宁省自然科学基金项目 201202033

详细信息

作者简介:
徐春光(1977—)，男，博士, 高级工程师

通讯作者:
刘君, liujun65@dlut.edu.cn

中图分类号: O354
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- 文章访问数: 4217
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- 被引次数: 0
出版历程
- 收稿日期: 2014-11-10
- 修回日期: 2015-03-30
- 刊出日期: 2016-05-25

An accurate conservative interpolation method for the mixed gridbased on the intersection of grid cells

School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, Liaoning, China

摘要

摘要: 基于网格切割思想，发展了二维/三维混合网格条件下的单元相交算法，可精确计算任意两个多边形/多面体的交集。在此基础上，实现了基于单元相交(CIB/DC)的精确守恒插值算法。二维和三维验证算例表明，该方法能够保证插值过程中计算域内物理量的严格守恒，且具有比常规二阶插值更高的精度。
- 流体力学 /
- 守恒插值 /
- 单元相交 /
- 混合网格 /
- 局部超网格
Abstract: A method is presented for conservatively transferring cell-centered physical quantities from one mesh to another with second-order accuracy, which is well-suited for finite-volume methods that rely on cell-centered variables. The proposed methodology implements the cell-intersection algorithm of 2D/3D mixed grid based on the local supermesh idea, and is able to accurately calculate the intersection of any two polygons or polyhedrons, thus providing a basis for accurate conservative interpolation. The accuracy and the efficacy of the new method are demonstrated with multiple 2D and 3D numerical experiments. The test results show that this method ensures strict conservation of physical quantities in the interpolation process, and achieves a higher accuracy than that achieved by conventional second-order interpolation methods.
- fluid mechanics /
- conservative interpolation /
- cell-intersection /
- mixed grid /
- local supermesh

HTML全文

图 1 超网格示意图

Figure 1. Schematic of the supermesh

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图 2 二维网格切割示意图

Figure 2. Schematic of the two-dimensional grid cutting

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图 3 直线切割平面凸多边形

Figure 3. Schematic of a straight line cuttingplane convex polygon

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图 4 三维网格分解示意图

Figure 4. Schematic of the three dimensional mesh decomposition

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图 5 相交单元的搜索方法

Figure 5. Search method of intersection elements

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图 6 数值计算建模图

Figure 6. Geometry of the specimenused for simulation

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图 7 计算结果的误差比较

Figure 7. Different errors of computational results

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图 8 计算结果的积分比较

Figure 8. Different integrals of computational results

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图 9 数值计算建模图

Figure 9. Geometry of the specimen used for simulation

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图 10 插值方法的精度比较

Figure 10. Comparison of precision with different interpolation methods

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图 11 测试函数分布云图

Figure 11. Nephogram of different test functions

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图 12 插值方法的精度比较

Figure 12. Comparison of precision with different interpolation methods

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表 1 计算网格参数

Table 1. Parameters of the computational grid

序号	结构网格	非结构网格
序号	结构网格	节点数	单元数
1	33×33	695	1 260
2	65×65	2 593	4 928
3	129×129	10 044	19 574
4	257×257	39 687	78 348

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表 2 不同算例的守恒误差

Table 2. Conservation errors indifferent numerical cases

序号	二阶插值	守恒型二阶插值
1	3.724×10^-3	0
2	-1.447×10^-3	0
3	-3.985×10^-4	1×10^-14
4	5.636×10^-5	-2×10^-14

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表 3 计算网格参数

Table 3. Parameters of the computational grid

序号	网格1		网格2		dx
序号	节点数	单元数	节点数	单元数	dx
1	914	4 033	676	2 711	0.067
2	2 222	10 632	1 424	6 075	0.050
3	6 527	32 913	3 733	16 681	0.035
4	26 099	138 542	12 600	59 347	0.022

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参考文献(11)

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