基于格子玻尔兹曼法和浸没边界法的流固耦合算法及应用研究

项目名称： 基于格子玻尔兹曼法和浸没边界法的流固耦合算法及应用研究

项目编号： No.10872153

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 金属学与金属工艺

项目作者： 程永光

作者单位： 武汉大学

项目金额： 28万元

中文摘要： 用格子Boltzmann方法（LBM）求解浸没边界法（IBM）的流体方程可明显提高IBM的计算效率。本研究旨在发展针对柔性结构流固耦合问题和复杂边界问题的LBM与IBM的耦合算法。具体进展为：提出了一种具有较高精度和稳定性的局部迭代耦合思路和算法步骤；用典型的算例对该算法进行了详细验证分析，证明了其具有良好体积守恒和迭代增稳特性，能保证空间二阶精度；应用该算法对花形气球形状恢复、心脏瓣膜开合等流固耦合问题，以及高雷诺数（Re）圆柱突然启动和旋转等复杂边界问题进行模拟，增强了对这些物理现象的认识；提出了能增大LBM单网格Re的粘性抵消法，验证了其效果，揭示了其增稳原因；将二维浅水方程的LBM模型在GPU计算机上并行实现，成百倍提高计算效率。研究成果为进一步的LBM与IBM耦合算法的应用奠定了基础。

中文关键词： 格子Boltzmann方法;浸没边界法;流固耦合;算法

英文摘要： The efficiency of the immersed boundary method (IBM) may be improved evidently by incorporating the lattice Boltzmann method (LBM) for solving the fluid flow equations. The aim of this study is to develop an efficient coupling scheme of LBM and IBM for the fluid structure interactions (FSI) concerning flexible structures and the rigid body problems concerning complex geometries or moving boundaries. The progress may be summarized as follows. A new LBM-IBM coupling scheme based on the second-order forcing term of the LB equation and a local iterative procedure is proposed. The features of better volume conservation, stability improvement by iteration, and the second-order spatial accuracy are verified by simulating typical examples. The scheme is applied to the simulations of FSI problems such as the relaxation of a flower-shaped membrane and the opening and closing dynamics of the mitral valve leaves, and moving boundary problems such as the impulsively starting of a cylinder and the rotation of a cylinder, from which the mechanisms are studied in depth. A viscosity counteracting approach to enhance the stability of the LBM's BGK model is proposed, so that the high Reynolds flows can be simulated by some relatively coarse lattice. To improve the parallel efficiency of the LBM, the model for the two-dimensional shallow water flow is implemented in the graphic processing unit (GPU) computers and as the results the speedup of efficiency up to some hundreds can be achieved. These provide the possibility for further applications to practical problems.

英文关键词： lattice Boltzmann method;immersed bpundary method; fluid structure interaction; algorithm