代用電荷法による数値等角写像とポテンシャル流問題への応用  [in Japanese] Numerical Conformal Mappings by the Charge Simulation Method and Their Application to Potential Flow Problems  [in Japanese]

代用電荷法を適用して，非有界な多重連結領域D から，平行スリット領域，円弧スリット領域，放射スリット領域への等角写像w =f(z) の簡単で精度の高い数値計算法が得られる．条件f(∞)= ∞を課した等角写像によって，障害物の周囲の一様流，渦流，湧き出し流（または，吸い込み流）の解析が可能である．本論文では，v をD 内に与えられた有限な点として，条件f (v )= ∞を課した数値等角写像の方法を提案する．このような等角写像によって，渦対流，湧き出し・吸い込み対流等の解析が可能になる．In this paper,we propose a method of conformal mapping w =f (z) of an unbounded multiply-connected domain D subject to the condition f(v) = ∞,where v is a given finite point in the problem domain.In the method,we reduce the mapping problem to a Dirichlet problem of a pair of conjugate harmonic functions and approximate them,using the charge simulation method,by a linear combination of complex logarithmic functions.The method can be applied to the analysis of a potential flow with a vortex pair past obstacles.A typical example shows the effectiveness of the method.Besides,the idea described here is applicable to some other comformal mappings which are important in potential flow problems.

In this paper, we propose a method of conformal mapping w = f (z) of an unbounded multiply-connected domain D subject to the condition f (∞) = ∞, where v is a given finite point in the problem domain. In the method, we reduce the mapping problem to a Dirichlet problem of a pair of conjugate harmonic functions and approximate them, using the charge simulation method, by a linear combination of complex logarithmic functions. The method can be applied to the analysis of a potential flow with a vortex pair past obstacles. A typical example shows the effectiveness of the method. Besides, the idea described here is applicable to some other comformal mappings which are important in potential flow problems.