High accuracy finite element method for flow problem with moving boundary and relative topics

动边界流动问题的高精度有限元方法及相关主题

• 批准号: 21540122
• 负责人: OHMORI Katsushi
• 金额: $ 2.91万
• 依托单位: University of Toyama
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540122/
• 关键词: 自由界面問題; 有限要素法; フラックス・フリー有限要素法; Semi-Lagrange Galerkin特性関数法; 表面張力; 反応拡散近似; 移動境界問題; Semi-Lagrange Galerkin特性有限要素法; Semi-Lagrange Galerkin法; 自由境界問題; 応用数学; 数値解析; 流体力学; 自由界面問題; 有限要素法; フラックス・フリー有限要素法; Semi-Lagrange Galerkin特性関数法; 表面張力; 反応拡散近似; 移動境界問題; Semi-Lagrange Galerkin特性有限要素法; Semi-Lagrange Galerkin法; 自由境界問題; 応用数学; 数値解析; 流体力学

In this research we considered the flux-free finite element method for incompressible two-fluid flows and we gave the mathematical considerlation for the mass conservation, error estimates and the convergence of the approximate solution of the flux-free finite element method for the genelarized Stokes interface problem in the case of discontinuous viscosity and density.Okumura considered the free-interface flow problem using the SLG characteristic finite element method with the Hermite element and the surface tension effect by the CSF method. Murakawa treated a moving boundary problem with triple-junction points. He provided a weak formulation of the problem which implicitly involves the information of the moving boundaries. Moreover, he proposed and analyzed an efficient numerical method for caputuring the moving boundaries. Yamaguchi had by analytic semigroup theory that mind solution of the Cauchy problem of penalized Navier-Stokes equations converges to that of original problem when penalty parameter tends to zero.

在这项研究中，我们考虑了不可压缩的两流体流的无通量有限元方法，我们给出了数学考虑的数学考虑，以进行质量保护，错误估计，误差和无限元元素的近似解决方案的收敛性，用于基因层化的Stokes互动问题，使用连续的粘度和密度的Flow frovister.okumura flow.okumura flow.okumura flow.okumura flow frovister.okumura flow.akumura。 CSF方法通过HERMITE元素和表面张力效应。村上用三结点处理了一个移动的边界问题。他提供了该问题的薄弱表述，该问题隐含地涉及移动边界的信息。此外，他提出并分析了一种有效的数值方法来限制移动界限。 Yamaguchi通过分析半群理论，即在惩罚参数往往为零时，cauchy cauchy问题的思维解决方案会收敛到原始问题。