有限元方法入门
有一个立方体裂隙岩石块；问题是：
- 如何模拟流体从顶部到底部或从左侧到右侧的流动？
- FEA (FEM,...) 是唯一实用的解决方案吗？
- 如果对于上述问题在最简单的条件下是这样的话，也就是说，流动只能通过裂缝发生；基质与流体之间无相互作用；等等如何使用FEA进行快速模拟？
- 这实用吗？具有 FEA 专业知识的人可以在几分钟内完成此操作吗？假设已经生成了合适的网格。
- 如果不，您会建议如何快速入门以解决此类简单的案例？
- 有没有人有类似问题的经验（流建模）；如果是的话，您使用了什么以及如何完成这项工作？
There is a cubic block of fractured rock; the question is:
- how to simulate fluid flow from top-side to down-side or left-side to right-side?
- Is FEA (FEM,...) the only practical solution?
- If so for the question above in its simplest conditions, that is, flow can happen only through fractures; no interaction between matrix and the fluid; etc etc how to have a quick simulation with FEA?
- Is this practical someone with professionality in FEA could do this in a few minutes? Suppose there is already a suitable mesh generated.
- If not what would you recommend to get started rapidly to be able to solve such simple cases?
- Is there anybody having experience with similar problem (flow modeling); if so what did you use and how did you fulfilled the job?
Note that we are aware of availability of many FEM packages e.g., FEniCS, OpenFoam, ....
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您的问题涉及多孔介质（例如岩石）中的流体模拟。
我强烈建议使用 LBM 而不是基于 FEM 的方法。 LBM 本质上模拟多孔介质中的流动。 Phys Review E 包含有关该方法的出版物。更吸引人的是，LBM 还可以轻松地在 GPU 上并行化。
Your question refers to simulation of the fluid in the porous medium, e.g. the rock.
I highly recommend using LBM instead of FEM-based methods. LBM simulates the flow in porous media by nature. Phys Review E contains publications about that approach. What is even more attractive, LBM can be also easily parallelized on GPU.
有许多数值技术可用于解决此问题，有限元可能是最常见的。如果您已经有了流体流动域的网格（大概是岩石中的空隙/裂缝），那么使用几乎任何 CFD 软件包（基于有限元或非有限元）设置和运行流动模型将非常简单，而且大多数人任何接触过 FEA 的人都应该能够做到。我假设您想更详细地了解岩石内的流体流动，而不仅仅是评估岩石对某些较大流动域中流动的影响。在后一种情况下，还有其他可能更具计算效率的方法。
There are a number of numerical techniques that could be used to solve this problem, finite elements being probably the most common. If you have a mesh of the fluid flow domain already (presumably the voids/cracks in the rock) it would be very straightforward to set up and run the flow model with pretty much any CFD package (finite element based or not) and most people with any exposure to FEA should be able to do it. I am assuming that you want to understand the fluid flow within the rock in some detail, rather than just evaluate the effects of the rock on the flow in some larger flow domain. In the latter case, there are other approaches which might be more computationally efficient.
您可以使用达西定律的一维形式。
You could use the one-dimensional form of Darcy's Law.