基于投影浸入边界法的流固耦合计算模型

Numerical Investigation of Fluid-Structure Interaction Using Projected Immersed Boundary Method

针对建立的刚体和流体相互作用的浸入边界法数学模型,借助求解不可压缩N-S方程组的分步投影方法的思想来求解基于浸入边界法的耦合系统方程.在空间离散上,对流项采用Quick格式,扩散项采用中心差分格式.时间推进采用显式欧拉法,固体对流体的作用力源项引入流体体积(VOF)方法中的体积比函数,通过龙贝格算法高效求解每个网格单元中浸入刚体所占的体积比.利用VC++编写投影浸入边界法的数值计算程序,并以单圆柱绕流为基准数值算例,通过与其他文献和实验结果的对比,验证了数值计算结果的准确性和可靠性,并进一步分析了不同雷诺数下圆柱绕流场的涡结构分布特征.

A mathematical model describing the interaction between immersed rigid body and fluid was established and was solved using the projection step method similar to the fractional step method for solving the incompressible Navier-Stokes equation. The volume ratio of a fluid grid was introduced to consider the effect of immersed rigid body, which was calculated by Romberg algorithm effectively. According to the numerical method, the corresponding numerical calculation program was written by C ＋ ＋ language. The reliability of solving the governing equation of projected immersed boundary method （IBM） was validated by the basic numerical example of flow over a circular cylinder. Finally, the distributions of the velocity field and the pressure field as well as the vortex structures were analyzed in different Reynolds numbers.