Regards all !:
I think this could be an interesting thread for a discussion, or perhaps someone may have the definitive answer yet,
When simulating some of the physical phenomena which can be simulated in COMSOL, using the different included modeules; ( e.g the Semiconductor, Microfluidics, MEMS, Heat Transfer, Molecular Flow, Electrodeposition, Electrochemestry, CFD, etc, modules... )
What is the limit (in the direction to the atomic scale) for which the results can still be considered as valids ?
I mean, Is kind of intuitive to think that if we try to simulate a tiny structure of a several atoms thick, the results provided by the simulation won't have any real meaning. But, What is the threshold of size speaking, for instance, of a micro/nano structure with this FEA software ?
Regards all :) !
I think the best answer is within the definition of continuum. As it says continuum approach is valid up to the point (infinitesimal volume) for which you can still assume that point is continuous. If the length is comparable to discrete particle then FEM or CFD is not valid anymore. You may still model them but modified constitutive equation may need to be written with added effects of all the physics that gonna be prominent at that length scale.
I think the best answer is within the definition of continuum. As it says continuum approach is valid up to the point (infinitesimal volume) for which you can still assume that point is continuous. If the length is comparable to discrete particle then FEM or CFD is not valid anymore. You may still model them but modified constitutive equation may need to be written with added effects of all the physics that gonna be prominent at that length scale.
The answer does not depend on the software but on the mathematical model. Provided you write the mathematical problem is governed by a system of PDE, all is computed within the continuum hypothesis and, therefore, to assess the validity of the assumption you should see at the ratio of your characteristic lenght to the so-called mean free path. For example, in case the medium of the problem is a fluid we define such ratio as Knudsen number. Of course, problems governed by PDEs exist in several fields and we always assume that a derivative exists, that is the variable is continuum.
Just a final note, in Finite element wherein a weak form of the equations is formulated, also within the continuum hypothesis you can work with discontinuous functions.
Since the question is not directly related to the COMSOL only, to satisfy the bottom limit in dimensions of a physical structure to be simulated in COMSOL Multiphysics, actually in COMSOL there is possibility to apply the lower-dimension postprocessing and the thin layer can be implemented. When postprocessing a simulation that contains thin walls modeled as surfaces or layers with an assigned mathematical thickness (rather than a geometric thickness), you will occasionally see different results when plotting on different types of entities. This means it’s important to be careful in cases that we refer to as lower-dimension postprocessing. We should highlight here that in the COMSOL software, a “thin layer” refers to a surface where physics will be solved by mathematically accounting for the real thickness of a wall instead of meshing it. These layers are treated as boundaries, while the surrounding area or areas are treated as domains. The benefit of using thin layer modeling — especially in multiphysics scenarios — is that it reduces computational time by circumventing the need to mesh a thin 3D layer. Lower-dimension postprocessing is a powerful tool that enables you to analyze results on one or both sides of a thin layer and is used for modeling electrical, mechanical, fluid, and chemical applications. Also recall that unexpected discontinuities may appear in a plot for several reasons when using lower-dimension postprocessing.
I hope it is helpful for you.
All the best.
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