Based on finite volume method, a mathematical model is built to present the 3D motion for incompressible viscous fluid. Numerical simulation research is carried out for the flow-around-cylinder field under the laminar flow (Re=100 )and turbulent flow (Re=3 900)by introducing and enforcing non-slip solid wall boundary conditions of immersed boundary method and Smagorinsky-Lilly sub-grid model of large eddy simulation. It is proved that the above method simulates unsteady flow around cylinder field well. The downstream flow field of the cylinder shows clear Karman vortexes without mixing under laminar flow. However, under the turbulent flow(Re=3 900),the downstream flow field of the cylinder presents higher mixing status, the turbulent intensity reaches the maximum value at 1.0D on the downstream side of the cylinder.%基于有限体积法建立描述不可压缩粘性流体三维运动的数学模型，引入浸入边界法的无滑移固定壁边界条件和大涡数值模拟的Smagorinsky-Lilly亚格子模型，针对层流(Re=100)和湍流(Re=3900)状态下的圆柱绕流流场进行数值模拟研究，验证结果表明该方法能较有效模拟非定常圆柱绕流流场的形态。在层流状态下圆柱体下游存在形态清晰的卡门涡街结构且无明显的掺混现象；在Re=3900的湍流状态下圆柱下游的掺混现象显著增强，圆柱下游约1.0 D处的脉动强度达到最大值。
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