In this paper, a new hybrid numerical approach is presented that couples “ghost cell” based immersed boundary (IB) method with the finite volume lattice Boltzmann method (FVLBM). In the implementation process, the grid cells are classified into three types, i.e., “”, “” and “”, where the “” is the first layer of “” near the “”. As the wall boundary condition is reflected in the “”, the high–accuracy reconstruction of variables in it will be the key point of present approach. Then, a FVLBM scheme is used to update the distribution function in the “”, and a least square interpolation based formulation is derived to construct the distribution functions in it. Further, the bounce–back scheme embedded in the streaming–collision lattice Boltzmann method will be employed as the wall boundary condition. Besides, for the class of moving boundary problems, the construction of the distribution function in the “” is also considered. A number of typical benchmarking incompressible viscous fluid flows over both stationary and moving objects are simulated to justify the present method, using obstacles ranging from a stationary and a translating circular cylinders, a rotationally oscillating cylinder, to two more complex flows around an oscillating cylinder in the stationary fluid and in the free–stream. Besides, the temporal and spatial accuracy also are testified by the simulation of Taylor–Couette flow. The obtained accurate simulation results demonstrate the capability of the present hybrid IB–FVLBM for computer simulations of both stationary and moving boundary problems in the incompressible flow regime.

中文翻译：

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使用最小二乘辅助“鬼细胞”技术增强耦合浸没边界有限体积格子玻尔兹曼方法 (IB-FVLBM)

本文提出了一种新的混合数值方法，将基于“幽灵细胞”的浸没边界（IB）方法与有限体积格子玻尔兹曼方法（FVLBM）相结合。在实现过程中，网格单元分为“”、“”和“”三种类型，其中“”为“”附近的第一层“”。由于壁面边界条件反映在“”中，其中变量的高精度重建将是本方法的关键点。然后，使用FVLBM方案更新“”中的分布函数，并导出基于最小二乘插值的公式来构造其中的分布函数。此外，流碰撞格子玻尔兹曼方法中嵌入的反弹方案将被用作壁边界条件。此外，对于一类动边界问题，还考虑了“”中分布函数的构造。模拟了静止和运动物体上的许多典型基准不可压缩粘性流体流动，以证明本方法的合理性，使用的障碍物范围从静止和平移的圆柱体、旋转振荡圆柱体到围绕振荡圆柱体的两个更复杂的流动静止流体和自由流。此外，泰勒-库埃特流的模拟也证明了时间和空间的准确性。获得的精确模拟结果证明了当前混合 IB-FVLBM 对不可压缩流态中的静态和移动边界问题进行计算机模拟的能力。