流体の自由表面問題における数値解析では、境界や流体場内部で満 たすべき微分方程式がまず存在し、これを重みつき残差法を用いて離 散化して解くという、いわばガラーキン法としての扱いが一般的に行 われている。しかし、粘性流体では変分原理は成り立たないものの、 完全流体に限れば、変分原理が成り立つことが明らかにされている。%This paper proposes a finite element method for nonlinear sloshing analysis of the perfect fluid in free-form containers. In this paper, the discrete governing equations of free surface flows are derived based on the variational principle. The energy functional is denoted by the volume integration of the Bernoulli's pressure equation, and by descritizing this functional previously, i.e. by applying the Ritz method, the governing equations are easily obtained. The numerical examples are presented for liquid-sloshing in a circular container. Furthermore, the sloshing vibration tests for the water tanks with variously inclined side walls are conducted, and the test results are compared with the analytical results obtained by the proposed method. Through these results, the effectiveness of the proposed method is confirmed.
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