基于特征分裂有限元准隐格式的共轭传热整体耦合数值模拟方法

共轭传热现象在科学和工程领域中大量存在. 随着计算能力的发展, 对共轭传热现象进行准确有效的数值模拟, 成为科学研究和工程设计上的重要挑战.共轭传热数值模拟的方法可以分为两大类: 分区耦合和整体耦合.本文采用有限元法对共轭传热问题进行整体耦合模拟. 固体传热求解采用标准的伽辽金有限元方法.流动求解采用基于特征分裂的有限元方法. 该方法是一种重要的求解流动问题的有限元方法, 可以使用等阶有限元. 该方法的准隐格式与其他格式相比, 具有时间步长大的特点. 将稳定项中的时间步长与全局时间步长分开, 改进了准隐格式的稳定性. 基于改进的特征分裂有限元方法的准隐格式, 发展了一种层流共轭传热数值模拟的整体耦合方法. 采用这种方法可以将流体计算域和固体计算域作为一个整体划分有限元网格, 并且所有变量都可以采用相同的插值函数, 从而有利于程序的实现. 通过对典型问题的模拟, 验证了这种方法的准确性. 本工作还研究了固体区域时间步长对定常共轭传热问题数值模拟收敛性的影响. 

A MONOLITHIC METHOD FOR SIMULATING CONJUGATE HEAT TRANSFER VIA QUASI-IMPLICIT SCHEME OF CHARACTERISTIC-BASED SPLIT FINITE ELEMENT

Conjugate heat transfer is widely present in the fields of science and engineering. With the development of computing power, the accurate and effective numerical simulation of conjugate heat transfer has become a major challenge in scientific research and engineering design. The method of numerical simulation of conjugate heat transfer can be divided into two main categories: partitioned method and monolithic method. Each of these methods has its pros and cons. We have developed a monolithic method for simulating the conjugate heat transfer between solid and incompressible laminar flows with the finite element method. Heat conduction in solid is solved by the standard Galerkin finite element method. The flow solution adopts the characteristic-based split finite element method (CBS). This method is an important finite element method for solving flow problems, and equal-order finite elements can be used. Compared with semi-implicit and CBS-AC schemes, the quasi-implicit scheme of this method can adopt a larger time-step. The stability of the quasi-implicit scheme is improved by distinguishing the time step in the stabilization item from the global time step. Based on the quasi-implicit scheme of the improved CBS method, a monolithic method of conjugate heat transfer numerical simulation has been developed. In this way, the fluid part and solid part of the computational domain can be divided into finite element meshes as a whole, and the equal-order interpolation functions can be used for all variables, thus facilitating the realization of the program. The accuracy of this method is validated by simulating the benchmark problems. The effect of the time step for the solid domain on the convergence of steady conjugate heat transfer simulation has also been studied.