How to discretize the pressure gradient for curvilinear MAC grids
How to discretize the pressure gradient for curvilinear MAC grids
复制标题
如何离散化曲线 MAC 网格的压力梯度
DOI：
10.1016/0021-9991(92)90208-g
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发表时间：
1992
影响因子：
4.1
通讯作者：
H. Kapitza
中科院分区：
文献类型：
--
作者：
R. Bernard;H. Kapitza
曲线坐标对于用标记单元格（MAC）进行不可压缩流计算存在一定的困难。其中包括关于压力梯度导数离散化的问题，在保持质量守恒的同时应保持不旋转。本文考察了边界附近的压力导数和整个流动的坐标导数的替代近似。测试了几种替代方案的组合在不增加涡度的情况下消除连续性违规的能力，这些通道已经安装了非正交MAC网格。这些组合中的每一种都实现了质量守恒，但其中只有一种使压力梯度有效地无旋转。后一种条件是通过在整个流动过程中对坐标导数和压力导数使用相同的近似来实现的，并且通过在边界附近对边界外方向的模糊导数使用单侧近似来实现。
Curvilinear coordinates present certain difficulties for incompressible flow calculations with marker-and-cell (MAC) grids. Among these are questions regarding the discretization of derivatives in the pressure gradient, which should remain irrotational while maintaining conservation of mass. This paper examines alternative approximations for pressure derivatives next to the boundaries and for coordinate derivatives throughout the flow. Several combinations of alternatives are tested for their ability to remove continuity violations, without adding vorticity, in channels that have been fitted with nonorthogonal MAC grids. Each of these combinations achieves conservation of mass, but only one of them makes the pressure gradient effectively irrotational. The latter condition is achieved by using identical approximations for coordinate derivatives and pressure derivatives throughout the flow, and by using one-sided approximations next to the boundaries for ambiguous derivatives in the off-boundary direction.