On a Method of Successive Approximations applied to the Axisymmetric Flows of an Incompressible Perfect Fluid

概要

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The fundamental equation for the steady axisymmetric flow of an incompressible inviscid fluid is expressed in a complex form as: 〓F/(〓ζ^^-) = (F-F^^-)/2(ζ-ζ^^-)) We here replace this by the following approximate equation: F_N = ∫(F_(N-1)-F^^-_<N-1>)/2(ζ-ζ^^-)dζ^^-+g_N(ζ), where F_N and F_<N-1> are the Nth and the (N-1)th approximations of the complex velocity potential F respectively, and g_N(ζ) is an appropriate complementary function of ζ. Treatment of this equation is very simple and its validity is ascertained by numerical calculations for the cases of a sphere and prolate spheroid for which exact solutions are already known. In the case of a sphere, approximate solutions converge uniformly to the exact one, while in the case of a prolate spheroid it is seen that the velocity potential on the surface is rather rapidly improved step by step.
社団法人日本物理学会の論文
1959-12-05