流体力学諸問題の一離散化解析 (その2)

三角形一次要素を用いた流れ関数による非圧縮粘性流れの有限要素解析

抄録

In the previous paper the numerical method of analysis of imcompressible viscous fluid problems was proposed. As velocities and pressure are adopted as the unknown values, it is believed that this appraoch may be very effective in analysis of the three dimensional flow problems. As it was demonstrated, the main feature of that method is the use of the lower order shape function in evaluation of element stiffness matrices.
Following the same line the two dimensional viscous flow problems are solved by using stream function in this paper. In the present analysis element matrices were derived from the hybrid variational principle of Hellinger-Reissner type which was used by K. Kondou in his plate bending analysis.
Using newly derived elements, the flow in a square cavity and the flow around a circular, cylinder are solved as examples. In the former problem the flow patterns are analyzed up to Reynolds number of 3200 and in the latter one the drag coefficients are calculated.
Results obtained in these analyses duly showed validity of the present method in comparison with the existing finite element or finite difference method.