多连通区域到狭缝圆环域的共形映射计算法
Numerical Conformal Mappings From Multiply Connected Regions Onto Annular Domains With Slits
赵鑫 1吕毅斌1
作者信息
- 1. 昆明理工大学 理学院,昆明 650500
- 折叠
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.
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.
关键词
共形映射/模拟电荷法/有界高连通度区域/BiCR法/螺旋点涡Key words
conformal mapping/charge simulation method/bounded high connectivity regions/BiCR method/spiral point vortex引用本文复制引用
基金项目
国家自然科学基金(11461037)
云南省基础研究计划(202101BE070001-050)
出版年
2024
国家科技期刊平台
NSTL
万方数据