生成項および仮想質量力が二流体モデルの数学的性質に及ぼす影響 : 第1報, 重力項の影響

概要

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According to mathematical theorems on initial-value problem, real-valued characteristic roots are necessary for a system of partial differential equations. However, a one-dimensional, one-pressure two-fluid model has complex-valued characteristic root, so that it is called mathematically ill-posed. Up to the present, eigenvalue analysis of a two-fluid model has been conducted only for a simplified two-fluid model without any source terms. Although these simplified analyses can yield a necessary condition for well-posedness, they cannot give a sufficient condition. A necessary and sufficient condition can be obtained if and only if the eigenvalues of a complete two-fluid model with source terms are evaluated. Furthermore, numerical stability of the two-fluid model is also affected by source terms. The examination of source terms is, hence, indispensable to clarify the mathematical and numerical nature of a two-fluid model. In this report, the method to examine the mathematical nature of a complete two-fluid model with source terms is presented. Based on this method, it is revealed that the degree of ill-posedness of the two-fluid model is greatly affected by gravity.
社団法人日本機械学会の論文
1998-08-25