Finite Element Method for Computational Fluid Dynamics with Turbulent Heat Transfer

数值模拟被广泛用于预测各种技术设备中热流体的行为。数值模拟中最大的问题是如何对实际技术设备的复杂边界形状进行数值处理。解决上述问题的数值方法是有限元方法，它易于建立包括前后处理在内的统一的流动分析系统。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)有效满足连续性方程的数值算法；(2)单元系数矩阵的有效计算。应用速度和Bernoulli函数的同时松弛方法和单元系数矩阵的积分分析公式，提出了一种新的适合于大型热流体数值模拟的广义简化标记和单元(GSMAC)方法。为了验证本文的数值方法，作者对以下问题进行了数值计算：(1)同心水平圆环内的自然对流，(2)旋转辊周围的流动，(3)导电流体在两平行平板之间的入口流动，得到了有效的结果。近年来，湍流换热的数值计算方法大多采用大涡模拟(LES)。传统的大涡模拟主要采用谱方法和有限差分法进行分析。将大涡模拟引入GSMAC有限元方法，对平行平板间的湍流流动进行了数值分析。这证实了本数值方法在考虑湍流换热的计算流体力学方面取得了显著的成果。

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.