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Numerical Conformal Mappings by the Charge Simulation Method and Their Applications to Fluid Mechanics

电荷模拟方法的数值共形映射及其在流体力学中的应用

基本信息

批准号：
15340033
负责人：
AMANO Kaname
金额：
$ 5.06万
依托单位：
Ehime University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2005
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15340033/
关键词：
charge simulation method Laplace's equation fundamental solution numerical conformal mapping multiply connected domain potential flow numerical analysis complex analysis

项目摘要

The numerical conformal mapping has been an important subject in computational and applied mathematics. Our major concern is to develop new methods of numerical conformal mappings by the charge simulation method (or the fundamental solution method) and apply them to potential flow problems.1.We constructed approximate mapping functions of the conformal mapping w= f(z) of an unbounded multiply connected domains D onto the unbounded canonical slit domains of Nehari (Mc-Graw Hill, 1952) under the condition f(v) = ∞, where v is a finite point given in the problem domain. They were applied to the problem of potential flows past obstacles caused by a dipole source, a pair of positive and negative vortexes or a pair of point source and sink.2.We constructed by the charge simulation method approximate mapping functions of the conformal mapping of bounded multiply connected domains onto all the unbounded and bounded canonical slit domains of Nehari.3.We proposed a new technique to apply the charge simulation method to a nonlinear compressible fluid flow problem. We also proposed a fundamental solution method for viscous flow problems with obstacles in a periodic array, which gives an approximate solution by a linear combination of periodic fundamental solutions.4.We proved the convergence of the approximate mapping function obtained by the charge simulation method.Many other interesting results were obtained in relation to methods of numerical computation and thier application to fluid mechanics.

数值保角变换一直是计算数学和应用数学中的一个重要课题。我们主要关注的是用电荷模拟方法来发展数值共形映射的新方法1.构造了无界多连通域D的保角映射w= f（z）到Nehari的无界正则狭缝域的近似映射函数（Mc-Graw Hill，1952）在f（v）= ∞的条件下，其中v是问题域中给定的有限点。它们被应用于由偶极子源引起的通过障碍物的势流问题，2.利用电荷模拟方法构造了有界多连通域到所有无界和有界正则Nehari缝域的共形映射的近似映射函数; 3.提出了一种新的电荷模拟方法非线性可压缩流体流动问题。我们还提出了一种基本解方法，它通过周期基本解的线性组合给出了粘性流动问题的近似解。4.我们证明了用电荷模拟方法得到的近似映射函数的收敛性。在数值计算方法及其在流体力学中的应用方面，得到了许多有趣的结果。