流体力学諸問題の一離散化解析(その1)

概要

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Recently the finite element method for analysis of flow problems has been established and a number of important contributions are being reported every year all over the world. It is common practice to use the higher order shape functions for these finite element flow analysis. Use of the higher order shape functions, however, may present a serious problem on computing time and cost in practice and it is believed that this situation will be more critical in case of flow analysis than in case of nonlinear analysis of solid mechanics problems. In view of such a situation, use of the lower order shape functions will be proposed in the finite element analysis of flow problems in this paper. In this approach, the higher derivative of velocity components, for example, will be approximated by the finite difference expression of the lower order derivatives. Therefore, it is expected that computing time for matrix manipulation will be considerably reduced. So far, application of this method has been made to analysis of KdV equation in the shallow water wave, steady creep flow and the potential flow problems. Results of these analysis have duly proved validity of this method. In this paper application will be attempted to analysis of the Navier-Stokes equation and discussion will be presented in comparison with existing finite element method.
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