An immersed boundary technique for simulating complex flows with rigid boundary
An immersed boundary technique for simulating complex flows with rigid boundary
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DOI：
10.1016/j.compfluid.2005.09.004
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发表时间：
2007-02
影响因子：
2.8
通讯作者：
Shen-Wei Su;M. Lai;Chao-An Lin
中科院分区：
文献类型：
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作者：
Shen-Wei Su;M. Lai;Chao-An Lin
提出了一种新的模拟流动与固体边界相互作用的浸没边界技术。本制剂采用欧拉和拉格朗日变量的混合物，其中固体边界由嵌入欧拉流体域中并向其施加力的离散拉格朗日标记表示。拉格朗日标记和流体变量之间的相互作用通过简单的离散化Delta函数联系起来。数值积分是基于交错网格空间框架下的二阶分数步长方法。基于欧拉网格上的直接动量强迫，提出了一种新的拉格朗日标记上的力公式，该公式保证了中间时间步浸入边界上无滑移边界条件的满足。这种强迫过程涉及求解带状线性方程组，其未知数由拉格朗日标记上的边界力组成;因此，未知数的阶数比流体变量低一维。数值实验表明，所提出的力公式的稳定性限制没有改变，虽然所采用的数值格式的二阶精度下降到1.5阶。四个不同的测试问题模拟使用本技术（旋转环流，盖驱动的空腔和流动超过一个固定的圆筒和一个在线振荡的圆筒），并将结果与以前的实验和数值结果进行了比较。数值实验表明，该方法具有较好的精度和计算能力，可用于求解具有固定边界和移动边界的复杂几何流动问题。
A new immersed boundary (IB) technique for the simulation of flow interacting with solid boundary is presented. The present formulation employs a mixture of Eulerian and Lagrangian variables, where the solid boundary is represented by discrete Lagrangian markers embedding in and exerting forces to the Eulerian fluid domain. The interactions between the Lagrangian markers and the fluid variables are linked by a simple discretized delta function. The numerical integration is based on a second-order fractional step method under the staggered grid spatial framework. Based on the direct momentum forcing on the Eulerian grids, a new force formulation on the Lagrangian marker is proposed, which ensures the satisfaction of the no-slip boundary condition on the immersed boundary in the intermediate time step. This forcing procedure involves solving a banded linear system of equations whose unknowns consist of the boundary forces on the Lagrangian markers; thus, the order of the unknowns is one-dimensional lower than the fluid variables. Numerical experiments show that the stability limit is not altered by the proposed force formulation, though the second-order accuracy of the adopted numerical scheme is degraded to 1.5 order. Four different test problems are simulated using the present technique (rotating ring flow, lid-driven cavity and flows over a stationary cylinder and an in-line oscillating cylinder), and the results are compared with previous experimental and numerical results. The numerical evidences show the accuracy and the capability of the proposed method for solving complex geometry flow problems both with stationary and moving boundaries.