请教：LBM 简单poiseuille流的模拟

dzl1988

各位高手，小弟刚刚学习LBM，现在在学习编写一个简单poiseuille流的模拟，遇到一些问题：
我是想模拟poiseuille流从开始到充分发展这个过程，入口处，上下边界都是采用非平衡态外推格式，在出口边界也想用非平衡态外推格式，可是出口边界的宏观速度未知。如果改用充分发展边界处理格式，就是边界速度
u(Nx,j)=u(Nx-1,j),发现程序发散。请问各位高手，这个问题该如何解决？

zhuocs

边界处理采用非平衡态外推格式是没问题的，你再仔细检查下。

dzl1988

谢谢 这个问题好多天了 呵呵 问题前几天解决了 的确和2楼说的一样 是编程出问题了 个人觉得 格子boltzmann 中边界问题很重要额

erhu10

楼主能不能说明一下自己编程出现的问题，方便新学习的借鉴

erhu10

原帖由 dzl1988 于 2010-4-24 14:07 发表

                               
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谢谢 这个问题好多天了 呵呵 问题前几天解决了 的确和2楼说的一样 是编程出问题了 个人觉得 格子boltzmann 中边界问题很重要额

楼主求助，你的那个问题是怎么解决的？

luo@odu.edu

Poiseuille flow can be solved analytically, because the nonlinear term in the NS equation vanishes. The velocity  profile is a parabola (2nd order polynomial across the channel) thus the LBE can yield the analytic solution EXACTLY (under the condition that a constant body force is exerted along the streamwise direction). For this flow, the LBE leads to a set of algebraic equations of which the solution is the central differencing formula for the streamwise velocity u(y), 0 <= y <= 1. There is a "fake" slip velocity at the "wall" depending on the boundary conditions at the wall and the chosen location of the wall.

This is a very good exercise for everyone who is serious about learning LBE. By carrying out this exercise carefully, you can gain a good understanding of the LBE.

Computer won't help you to understand the LBE.

lwd1981

非平衡态外推格式一般没问题，也比较简单，就是收敛稍微有点慢，呵呵