Stability of approximate projection methods on cell-centered grids
Stability of approximate projection methods on cell-centered grids
复制标题
以单元为中心的网格上近似投影方法的稳定性
DOI：
10.1016/j.jcp.2004.09.005
复制
发表时间：
2005
影响因子：
4.1
通讯作者：
A. Fogelson
中科院分区：
文献类型：
--
作者：
R. Guy;A. Fogelson
投影法是求解不可压缩纳维-斯托克斯方程的一类流行方法。如果选择以单元为中心的网格，为了对平流项使用高分辨率方法，精确地执行投影是有问题的。一个有吸引力的替代方案是使用近似投影，其中要求速度仅近似离散地无发散。以细胞为中心的近似投影的稳定性对更新压力和计算压力梯度的方法高度敏感。这是通过分析模型问题并对纳维-斯托克斯方程进行数值模拟来证明的。
Projection methods are a popular class of methods for solving the incompressible Navier–Stokes equations. If a cell-centered grid is chosen, in order to use high-resolution methods for the advection terms, performing the projection exactly is problematic. An attractive alternative is to use an approximate projection, in which the velocity is required to be only approximately discretely divergence-free. The stability of the cell-centered, approximate projection is highly sensitive to the method used to update the pressure and compute the pressure gradient. This is demonstrated by analyzing a model problem and conducting numerical simulations of the Navier–Stokes equations.