Abstract
Although the finite difference method has been applied to various flow problems, it is well known that this method occasionally encounters difficulties for the analysis of the problem whose configuration is complicated. The authors, adopting the penalty finite element method, developed the two-dimensional thermal convection analysis code formerly. In this paper, it is extended to the axisymmetric and the three-dimensional code so that the three-dimensional effect can be taken into consideration to analyze variety of problems with high accuracy.In the penalty finite element method, the reduced integration technique is applied for the penalty term to avoid the phenomenon called locking. In this paper, it is shown for the axisymmetric analysis that the accuracy is lost in evaluating the penalty term by 1×1 Gauss point for the 4-node element, and that exact integration by 2×2 Gauss points leads the solutions to the locking. On the contrary, it is observed that the 9-node element with 2×2 Gauss points gives good solutions for various types of problems. And performed also is the three-dimensional analysis for a cavity flow and a duct flow.
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