多连通区域到狭缝圆环域的共形映射计算法

赵鑫; 吕毅斌

doi:10.21656/1000-0887.440134

多连通区域到狭缝圆环域的共形映射计算法

doi: 10.21656/1000-0887.440134

赵鑫,
吕毅斌^,

昆明理工大学理学院，昆明 650500

基金项目:

国家自然科学基金 11461037

云南省基础研究计划 202101BE070001-050

详细信息

作者简介:
赵鑫(1998—)，男，硕士生(E-mail: zhaoxin1@stu.kust.edu.cn)

通讯作者:
吕毅斌(1972—)，男，副教授，硕士生导师(通讯作者. E-mail: luyibin@kust.edu.cn)

中图分类号: O241
计量
- 文章访问数: 125
- HTML全文浏览量: 41
- PDF下载量: 33
- 被引次数: 0
出版历程
- 收稿日期: 2023-05-03
- 修回日期: 2023-11-06
- 刊出日期: 2024-02-01

Numerical Conformal Mappings From Multiply Connected Regions Onto Annular Domains With Slits

ZHAO Xin,
LÜ Yibin^,

Faculty of Science, Kunming University of Science and Technology, Kunming 650500, P.R.China

摘要

摘要: 基于模拟电荷法，研究了将具有高连通度的有界区域映射到带有对数螺旋狭缝单位圆环域的共形映射计算法.提出利用BiCR(bi-conjugate residual)算法求解由Dirichlet边界条件建立的约束方程组，得到模拟电荷，进而构造出高精度的近似共形映射函数.数值实验验证了该文算法的有效性，并成功将该共形映射计算法应用到绕流仿真模拟中，模拟了有界高连通度区域内螺旋点涡的绕流.
- 共形映射 /
- 模拟电荷法 /
- 有界高连通度区域 /
- BiCR法 /
- 螺旋点涡
Abstract: A numerical method was proposed based on the charge simulation method for calculating conformal mappings from the bounded high connectivity regions onto unit annular domains with logarithmic spiral slits. The bi-conjugate residual (BiCR) method was used to solve the constraint equation system acquired with the Dirichlet boundary conditions, obtain the simulated charge, and further construct a high-precision approximate conformal mapping function. Numerical examples show the effectiveness of the proposed method applied to simulate flow over the spiral point vortex in the bounded high connectivity domains.
- conformal mapping /
- charge simulation method /
- bounded high connectivity regions /
- BiCR method /
- spiral point vortex

HTML全文

图 1 基于模拟电荷法的有界高连通度区域共形映射

Figure 1. Conformal mappings of bounded high connectivity regions based on the charge simulation method

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图 2 有界10连通区域网格图

Figure 2. The grid diagram of bounded 10 connected domains

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图 3 带有对数螺旋狭缝的单位圆环

Figure 3. The unit circular ring with logarithmic spiral slits

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图 4 例1中共形映射误差曲线

Figure 4. The conformal mapping error curves in example 1

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图 5 例1中螺旋点涡的绕流模拟

Figure 5. Simulation of flow over the spiral point vortex in example 1

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图 6 有界16连通区域网格图

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 6. The grid diagram of bounded 16 connected domains

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图 7 带有对数螺旋狭缝的单位圆环

Figure 7. The unit circular ring with logarithmic spiral slits

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图 8 例2中共形映射误差曲线

Figure 8. The conformal mapping errors curves in example 2

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图 9 例2中螺旋点涡的绕流模拟

Figure 9. Simulation of flow over the spiral point vortex in example 2

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