格子玻尔兹曼法多块网格的交界结构优化研究

Optimization study of Multi-Block interface structure based on Lattice Boltzmann Method

基于格子玻尔兹曼方法LBM(Lattice Boltzmann Method)对多块网格方法(Multi-Block)的粗细网格交界结构进行了研究,提出了一种新的优化处理方案。解决了原有网格交界结构存在的三个问题,即两套插值运算造成的程序结构复杂的问题,存储前几个时间步的节点流场数据以备插值运算造成内存浪费的问题和基于时间插值结果进行空间插值计算造成插值误差积累的问题。用一次多点二维空间插值的方式,将原方法的空间和时间双插值,简并成一次空间插值。通过对经典的非定常的圆柱绕流算例和定常的标准顶盖方腔驱动流算例的仿真模拟,验证了交界面处质量、动量及应力的连续性以及网格交界面数据过渡的流畅度,最终验证了改进方法的正确性。数值模拟结果表明,改进后多块算法可实现局部网格细化,进一步推动LBM方法在实际工程问题中的应用。

An optimal plan of mesh interface between the coarse and fine mesh of Multi-Block method is proposed based on the Lattice Boltzmann Method in this paper.Three key problems in the original mesh interface are effectively solved,namely,the problem of complex programming due to two sets of interpolation operations,memory waste caused by the flow data of the several past time steps is stored for the time interpolation,and accumulative interpolation error due to spatial interpolated interpolation.A new kind of coarse mesh overlapping is developed,in which the interpolation of the original space and time is simplified into a spatial interpolation by means of two-dimensional multi-point spatial interpolation.Classic examples of unsteady flow around a circular cylinder and driven flow of square cavity are analysed.The continuity of mass,momentum and stress at the interface and smoothness of transition of the interface data are verified.The computational results show that the improved Multi-Block algorithm can realize the local mesh refinement,and further promote the application of LBM in practical engineering problems.