A level set‐based immersed interface method for solving incompressible viscous flows with the prescribed velocity at the boundary
A level set‐based immersed interface method for solving incompressible viscous flows with the prescribed velocity at the boundary
复制标题
基于水平集的浸入界面法求解边界处规定速度的不可压缩粘性流
DOI：
10.1002/fld.2018
复制
发表时间：
2009
影响因子：
1.8
通讯作者：
B. Khoo
中科院分区：
文献类型：
--
作者：
Z. Tan;K. Lim;B. Khoo
提出了一种二阶精度浸没界面法(IIM)，用于求解边界上给定速度的不可压N-S方程，推广了Le等人的浸没界面法。J·康普特。太棒了。2006；220：109-138)到边界的水平集表示，而不是使用均匀笛卡尔网格上的控制点的边界的拉格朗日表示。为了满足规定的速度边界条件，对流体施加浸没边界上的奇异力。这些力与压力的跳跃以及压力和速度的导数的跳跃有关，并通过使用局部Hermite三次样条插值来逼近。奇异力的强度是通过在每个时间步求解一个小的方程组来确定的。在交错笛卡尔网格上引入跳跃条件，用有限差分方法离散N-S方程，并用二阶精度投影法求解。数值结果表明，该方法能较好地模拟非规则区域的粘性流动。版权所有©2009 John Wiley&Sons，Ltd.
A second‐order accurate immersed interface method (IIM) is presented for solving the incompressible Navier–Stokes equations with the prescribed velocity at the boundary, which is an extension of the IIM of Le et al. (J. Comput. Phys. 2006; 220:109–138) to a level set representation of the boundary in place of the Lagrangian representation of the boundary using control points on a uniform Cartesian grid. In order to enforce the prescribed velocity boundary condition, the singular forces at the immersed boundary are applied on the fluid. These forces are related to the jump in pressure and the jumps in the derivatives of both the pressure and velocity, and are approximated via using the local Hermite cubic spline interpolation. The strength of singular forces is determined by solving a small system of equations at each time step. The Navier–Stokes equations are discretized via using finite difference method with the incorporation of jump conditions on a staggered Cartesian grid and solved by a second‐order accurate projection method. Numerical results demonstrate the accuracy and ability of the proposed method to simulate the viscous flows in irregular domains. Copyright © 2009 John Wiley & Sons, Ltd.