|
发表于 2013-7-28 21:51:17
|
显示全部楼层
回复 13# onesupeng 的帖子
Dear Onesupeng,
First, thank you very much for your illuminating discussion. I do enjoy reading it. However, this discussion also shows us that we have a huge problem in even talking about a specific, small problem.
Let's focus on the word "comparison" for now. It is absolutely essential that a COMPARISON is done with the EXACTLY identical flow conditions. Else it is should not be called a COMPARISON, certainly within the context of CFD. Thus one must be extremely careful when "compare" CFD with experimental results. In any event, (rigorous) comparison is an indispensable tool in CFD, and it appears that many still do not what it means.
Next, the Stokes flow, which consists of 2 equations: the (linear) momentum equation + the incompressibility condition. It is known that the solution for, say, a 2D cylinder in free space decays like (1/r), where r is the radial distant from the cylinder center. This means that the effect due to the (far field) boundary is also behaves like (1/r), thus decays too slowly. That explains why "blockage" matters so much in the flow, and this is not entirely based on just experience -- people in applied math. or PDEs would tell us they knew it all along. With this in mind, to solve the flow past a cylinder with very small Re, we need not only a good discretization scheme, but also an effective way to treat boundary conditions. More over, to enhance computational efficiency, we also need acceleration techniques (e.g., multigrid), which is not discussed here.
Within the context, the work of Labrosse & Lallemand show that LBE is a good second-order discretization scheme, while the work by Krafczyk and his student show that grid-refinement is necessary for the problem and it is doable with LBE. (Unfortunately, Krafczyk's work has never been published, it's in a student's thesis.) I apologize that my previous responses were not carefully qualified.
It is important to realize that one should not expect to use the so-called lattice BGK model (which is very silly scheme, by the way) with a uniform mesh and explicit time-stepping to solve all possible problems in CFD. However, some claim the contrary and they believe in magics, as we have seen on the forum. It is sad to see that many students are trying just to do that. My question is whether these students are pushed to do so, and they are simply lack of proper education. I only hope that our discussions would help these students.
Finally, I agree with your comments about benchmarks. A set of WELL-DEFINED benchmark problems are essential in CFD. Students must be taught how to conduct comparative studies. Comparison with experimental data is a much harder subject, which I shall say nothing.
[ 本帖最后由 luo@odu.edu 于 2013-7-28 22:22 编辑 ] |
|