Analysis of an iterative penalty method for Navier–Stokes equations with nonlinear slip boundary conditions
Analysis of an iterative penalty method for Navier–Stokes equations with nonlinear slip boundary conditions
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DOI：
10.1002/fld.3742
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发表时间：
2013-06
影响因子：
1.8
通讯作者：
X. Dai;Peipei Tang;Minghui Wu
中科院分区：
文献类型：
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作者：
X. Dai;Peipei Tang;Minghui Wu
当我们使用惩罚方法求解具有非线性滑移边界条件的Navier-Stokes方程时，惩罚参数λ应该足够小以产生准确的近似值，并且λ的选择取决于网格尺寸h。然而，如果λ太小，相关刚度矩阵的条件数就会变大，从而导致计算不稳定。本文设计了一种迭代惩罚方法，并给出了一些误差估计。在我们的算法中，我们可以使用一个不太小的惩罚参数，独立于h，以避免不稳定的计算。算例表明了该算法的有效性和有效性。版权所有©2012 John Wiley & Sons， Ltd。
When we use penalty method to solve Navier–Stokes equations with nonlinear slip boundary conditions, the penalty parameter ϵ should be sufficiently small to yield an accurate approximation and the choice of ϵ depends on the mesh size h. However, the condition number of the associated stiffness matrix becomes large if ϵ is too small, which leads to the unstable computation. In this paper, we design an iterative penalty method for the problem and give some error estimates. In our algorithm, we can use a not very small penalty parameter ϵ independent of h to avoid the unstable computation. Numerical examples are given to show that the algorithm is very effective and powerful. Copyright © 2012 John Wiley & Sons, Ltd.