为对浸入边界-格子Boltzmann方法框架(IB-LBM)下浸入边界点数量的设置提供依据,本文采用雷诺数Re=40和100下的圆柱绕流作为理论验证模型,对不同耦合网格比CRG(Coupling Ratio of Grid)下的计算稳定性进行研究。分别采用D_p4-p(4-point Piecewise Delta)函数和D_c4-p(4-point Cosine Delta)函数作为平滑函数,通过分析Re=40圆柱绕流充分发展后的流线分布、尾涡长度和阻力系数等指标,获得了在D_p4-p下CRG的相对稳定范围大致为0.2—2之间,在D_c4-p下相对稳定范围大致为1.5—2之间。在Re=100下,通过细分CRG对圆柱绕流进行计算,对照阻力系数的变化,与Re=40时的情况基本一致,表明D_p4-p有更宽的稳定取值范围,这为IB应用过程中合理选择Delta函数及相应的CRG取值提供了参考。

In order to provide the foundation for immersed boundary points setting in the Immersed Boundary-Lattice Boltzmann Model (IB-LBM) frame, the numerical stability with the different Coupling Ratio of Grid (CRG) between the IB and LBM is studied. As the theoretical model to be verified for the applicable coupling ratio, flows around a circular cylinder with the Reynolds number of Re=40 and 100 are calculated, respectively. The distribution of streamline, the length of wake vortex, and the drag coefficient are analyzed for the case of Re=40 with the 4-point Piecewise Delta function being adopted in IB, the calculating results indicate that an acceptable range for CRG is 0.2-2, it is also essentially true for the case of Re=100. However, a different CRG range of 1.5—2 is found while the 4-point Cosine Delta function is used, the fact indicates that the 4-point Piecewise Delta function has a wider range for setting CRG, it is of great value to the optimal choices for Delta function and corresponding CRG in the IB applications.