基于四叉树网格下的浸入边界-格子Boltzmann方法

Immersed boundary-lattice Boltzmann method based on quadtree grids

提出了一种基于非均匀四叉树网格下的浸入边界-格子Boltzmann方法。在不同层网格界面上,为了保证物理量的连续性,需要在时空方向上进行插值。由于四叉树同层网格在空间上步长相等、且相邻时间层上时间步长相等,所以在时空方向上采用平均值插值,这样做的优点是时空方向插值既可以达到二阶精度,又可以简化计算过程,节省资源,对任意边界加密下的网格,格子Boltzmann方法的实现比较容易。为了充分利用均匀笛卡尔网格的优势,物面边界的处理采用了速度修正法,与传统浸入边界-格子Boltzmann方法中的直接力法、动量交换法相比,无滑移边界条件得到了较好的保证。同时,把大涡模型加入到浸入边界-格子Boltzmann方法中,实现了在四叉树网格数据结构、边界处理技术、大涡模拟几种模型相结合下,绕障碍物的较大雷诺数流动的模拟。通过不可压缩粘性流中圆柱绕流算例验证,结果与其它方法结果吻合良好。

An immersed boundary-lattice Boltzmann method based on non-uniform quadtree grids is proposed in present paper.In order to retain continuous physical quantity,equal interval interpolation in temporal and spatial space is used on the different grid interface.Because quadtree grids have identical spatial size in the same grid level and identical temporal size in the neighbor temporal level,equal interval interpolation retains second-order accuracy in temporal and spatial space,has simple computational process,need less resource,and achieves utilization of arbitrary boundary refined grids in the lattice Boltzmann method.To take advantage of the merit of the Cartesian grid,the velocity correction method is adopted in immersed boundary,which ensures the non-slip boundary compared to the direct forcing method or the momentum exchange method in the conventional immersed boundary-lattice Boltzmann method.At the same time,the large-eddy simulation model is applied to immersed boundary-lattice Boltzmann method.In this paper,the proposed model combines with quardtree grids data structure,boundary treatment with large eddy simulation to simulate the flows with high Reynolds number around the obstacle.To validate these models,the incompressible flows around a circular cylinder with Re=200,1000,3900are simulated,and the simulation results agree well with those of other methods.