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首页> 外文期刊>International Journal of Heat and Mass Transfer >A modified, hybrid nodal-integral/finite-element method for 3D convection-diffusion problems in arbitrary geometries
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A modified, hybrid nodal-integral/finite-element method for 3D convection-diffusion problems in arbitrary geometries

机译：任意几何中的3D对流扩散问题的改进的混合节点积分/有限元方法

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摘要

A modified, hybrid nodal-integral/finite-element method (NI-FEM) is developed to solve the three-dimensional (3D), steady-state, convection-diffusion problems in arbitrary geometries. The hybrid NI-FEM takes advantage of the high efficiency of the conventional nodal-integral method (NIM) and the flexible mesh generation of the finite element method (FEM), which is applicable to arbitrary geometries. In this method, the computational domain is discretized into, for 3D problems, four-node tetrahedral elements and eight-node cuboid elements. The cuboid elements are used to discretize the interior region and regions adjacent to boundaries that are parallel to planes formed by two of the axes, while the tetrahedral elements are used to discretize the remaining irregular regions. The conventional NIM is used to develop difference equations for the transverse-averaged variables on the interface between two adjacent cuboid elements. The FEM is applied to develop algebraic equations for the node temperatures of tetrahedral elements. On the interface between two different kinds of elements, the transverse-averaged variable for the cuboid element is obtained by averaging the node values of its adjacent tetrahedral elements, while the heat flux for the tetrahedral element is calculated using the corresponding transverse-averaged variables of its adjacent cuboid element. The hybrid NI-FEM is developed to be solved using a matrix formulation for the entire domain rather than an iterative procedure, detailed derivations of which for the 3D case are presented in this paper. Using the NI-FEM developed here, 2D and 3D convection-diffusion test problems are solved, and the numerical results are compared to the exact (manufactured) solutions to determine the order, accuracy and efficiency of the method. Numerical scheme is found to be of, as expected, second order.
机译：提出了一种改进的混合节点积分/有限元混合方法（NI-FEM），以解决任意几何中的三维（3D）稳态对流扩散问题。混合NI-FEM充分利用了常规节点积分法（NIM）的高效率以及有限元方法（FEM）的灵活网格生成功能，该方法适用于任意几何形状。在这种方法中，对于3D问题，计算域被离散化为四节点四面体元素和八节点长方体元素。长方体元素用于离散内部区域和与平行于两个轴所形成的平面的边界相邻的区域，而四面体元素则用于离散其余的不规则区域。传统的NIM用于为两个相邻的长方体元素之间的界面上的横向平均变量开发差分方程。有限元法用于开发四面体单元节点温度的代数方程。在两种不同类型元素之间的界面上，长方体元素的横向平均变量是通过将其相邻四面体元素的节点值平均而获得的，而四面体元素的热通量则是使用相应的横向平均变量来计算的其相邻的长方体元素。混合NI-FEM的开发需要使用针对整个域的矩阵公式而不是迭代程序来解决，本文将针对3D情况详细介绍其衍生过程。使用此处开发的NI-FEM解决了2D和3D对流扩散测试问题，并将数值结果与精确的（制造的）解决方案进行比较，以确定该方法的顺序，准确性和效率。发现数值方案是预期的二阶。

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