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

数值保角映射一直是计算数学和应用数学中的一个重要课题。1.在f(V)=∞的条件下，我们构造了无界多连通区域D的共形映射w=f(Z)到Nehari(Mc-Graw Hill，1952)的无界正则狭缝区域上的近似映射函数，其中v是问题域中给出的一个有限点。我们利用电荷模拟方法构造了有界多连通区域的保角映射到Neharie的所有无界和有界正则缝隙区域上的近似映射函数。3.我们提出了一种新的方法将电荷模拟方法应用于非线性可压缩流体流动问题。我们还提出了周期阵列中带有障碍物的粘性流动问题的基本解方法，该方法通过周期基本解的线性组合来给出近似解。4.证明了由电荷模拟方法得到的近似映射函数的收敛。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。

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.