有限容积法与格子Boltzmann方法耦合模拟传热流动问题

自然界和工程领域中的许多物理现象的发生通常涵盖几个数量级的几何空间及时间范围, 我们将其统称为多尺度物理现象. 在模拟多尺度问题时, 如果仅采用宏观方法, 则会存在一些不足, 如无法预知微小部分的细节以及引入复杂的经验关联式; 如果仅采用介观/微观方法, 则需要消耗大量的计算资源. 构造宏观-介观、宏观-微观、宏观-介观-微观等多种层次上方法的耦合体系, 可以在很大程度上克服这些不足. 构造了宏观有限容积法(FVM)与介观格子Boltzmann方法(LBM)的耦合模型(CFVLBM), 给出了由宏观物理量重构密度分布函数和温度分布函数的两个重构算子, 解决了LBM与宏观方法耦合的关键难题. 选取二维、三维典型传热流动问题对耦合模型进行了考核, 计算结果同基准解符合得很好. 最后将CFVLBM应用于计算多孔介质内的复杂流动问题. 研究表明, 基于文中重构算子的CFVLBM可以准确有效地应用于模拟传热流动问题.

Coupling between FVM and LBM for heat transfer and fluid flow problems

Multiscale numerical simulation has been developed very fast in recent years. The convectional numerical approaches always focus on the macroscale and eliminate the effect of meso/microscale process. For complicated problems, some distinct limitations will occur, among whom the lack of detail for some local processes and the necessity of introduction empirical closures are especially obvious. These shortcomings may be overcome if we use meso/microscale methods. But if we use single meso/micro level model on the entire computational domain of a complicated problem, the required computer source is out of reality. By coupling macro/meso scale methods, macro/micro methods or macro/meso/micro methods, such difficulty can be, to a great extent, overcome. In coupling between the FVM and LBM, the key issue is how to effectively transform the macroscopic results of FVM into particle distribution function of LBM, i.e. how to find the reconstruction operator which can perform such transformation efficiently. Two analytic expressions of the reconstruction operators have been proposed for the exchange from density, velocity and temperature of FVM to the distribution functions of LBM. The two reconstruction operators are validated by the 2D, 3D heat transfer and fluid flow problems. All of the results are found to be in good agreement with benchmark solutions. At last, the CFVLBM is used to solve a complex flow involving porous media. The results show that the CFVLBM can not only predict the flow pattern in the whole computation domain, but also capture the flow characteristic near the airfoil or in the pore of porous media.