Finite Element Method for Computational Fluid Dynamics with Turbulent Heat Transfer

数值模拟是一种广泛应用于研究各种工艺装置中热流体行为的方法。数值模拟中最大的问题是如何在数值上处理实际技术装置复杂的边界形状。解决上述问题的数值方法是FEM (Finite Element method)，该方法易于建立包括前后配置在内的统一流动分析系统。然而，在有限元数值模拟中，以下问题成为一个严重的问题：(1)有效地满足连续性方程的数值算法；(2)单元系数矩阵的有效计算。运用速度与伯努利函数的同时松弛法和单元系数矩阵的综合分析公式，提出了一种适用于热流体大规模数值模拟的广义简化标记与单元法（GSMAC）。为了验证该数值方法，申请人对以下问题进行了数值计算：(1)同心水平环形环内的自然对流，(2)旋转轧辊周围的流动，(3)平行板间导电流体的入口流动，并得到了有效的结果。近年来，紊流换热的数值计算方法大多采用大涡模拟方法。传统的LES分析方法主要是频谱法和有限差分法。将LES引入GSMAC-FEM，对两个平行板间的湍流流动进行了数值分析。这证实了目前的数值方法在紊流传热计算流体力学方面取得了显著的成就。

A numerical simulation is extensively used as a procedure to prospect the behaviors of thermal fluids in each kind of technical devices. The largest problem in a numerical simulation is the way how to treat a complex boundary shape of actual technical devices numerically. The numerical method to resolve the above-mentioned problem is FEM (Finite Element Method), which is easy to establish a unified flow analysis system including pre-post disposition. However, in the numerical simulation using FEM the following subjects become a serious problem : (1) the numerical algorithms to satisfy the equation of continuity efficiently, (2) the effective calculation of element coefficient matrices. Using both the simultaneous relaxation method of velocity and Bernoulli function and the integrated analysis formula of element coefficient matrices, the applicant proposed so far a new GSMAC (Generalized Simplified Marker And Cell) method, which is proper for a large-scale numerical simulation for thermal fluids. In order to verify the present numerical method, the applicant calculated the following problems numerically : (1) natural convections in concentric horizontal anulli, (2) flows around a rotaring roll, (3) entrance flows of electrically conducting fluids between two parallel plates, and efficient results were obtained. In the recent years, most of numerical method for turbulent heat transfer have been calculated using LES (Large Eddy Simulation). The conventional LES is mostly analyzed by spectrum method and FDM (Finite Difference Method). Introducing LES into GSMAC-FEM, the turbulent flows between two parallel plates are analyzed numerically. This con-firms that the present numerical method has made remarkable achievements for computational fluid dynamics with turbulent heat transfer.