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I have been trying to make a biologically accurate 2D spatial model of tissue layers, where different physiological processes happen. This includes mainly chemical reactions, diffusion and fluxes over boundaries.

I am making this model in COMSOL Multiphysics, a finite element software package that solves different physics like reaction-diffusion systems, although for my question this might not be really relevant.

In my geometry, I have really small regions between the cells of the tissue layers. These regions serve as openings where diffusion can take place between the cells (junctions). The quality of the mesh is not great here and if I want to improve the quality (mainly by introducing more elements and such), my simulation time increases drastically. The lesser quality mesh also causes convergence to take longer. I added a picture of the geometry to give an idea. I tried different meshes, all with different qualities of the elements and the number of elements ranging from 16000 to 50000.

My background in FEM is really limited and I wanted to know if I can tackle this problem in such a way that it

  1. doesn't negatively affect the biology (keep the tissue domain sizes/problem etc as biologically accurate as possible),
  2. doesn't increase the simulation time drastically,
  3. give a better mesh quality.

So I really want to know what the best way to go is, since I have already thought of some things.

Can I go with the lesser quality mesh (which is not really bad, but not good either), so that I can keep the small regions for optimum biological accuracy and have a relatively small computation time (and hope I won't run into convergence errors). But maybe there are possibilities that I am missing, for instance: is it possible to make the small domain bigger and then add some kind of factor to the diffusion rates. In other words, if I want to make the domain twice as large, do I factor the diffusion rate with half? Is that even accurate in chemical/physical laws :S.

Hopefully I made the problem a bit clear and thank you greatly in advance for the help.

Cheers,

Mesh of the tissue model Mesh of the tissue model

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我知道这个帖子是几个月前发布的，但我不确定你是否找到了解决方案。

为了找到精度和计算时间之间的关系，您需要对模型进行网格分析，看看网格大小如何直接影响您期望获得的结果（孔隙压力、流体速度、应变等）。将允许您确定最适合您的特定问题的网格策略。

此外，您可能需要记住，材料的扩散速率将取决于孔径和渗透性（通过达西定律），因此取决于您为实施本构定律和您的问题所做的假设边界条件，您可能会简化/扩大模型中的一些较小域，只要它们在您之前做出的假设范围内。

于 2016-07-30T17:24:06.360 回答