Discussion Forum

Hi

I believe there is no "one answer", if I have such large scale difference I make aften my domains with interiour boundaries such that I mesh the regions with different densities. Often I use boundary mesh elements with very uneven shapes, but this depends on the model.

Basically the mesh is a "sampling" of your equations, if these have a very steep gradient along Y and a small gradient along Y, you can use safely a elongated mesh, long along Y and very short along X.

The average mesh quality is for homogenious or isotropic mesh cases, a COMSOL mesh quality of 1e-5 can be perfectly OK for a highly anisotropic case provided that the linear mesh quality is respected along the different directions.

One way to check your results is to solve for mesh density of 1 and then of 2 (or 0.5) and look at the resultes, by how much do they change

When I talk about sampling, it is not only spatial sampling, but also transient, particularly in diffusion equation cases with step wise boundary conditions (often along constant temperature T or concentration C boundaries, for the rest of the environment at "0" initial conditions

For the oscillations, check the Reference guide about stabilization techniques

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Good luck
Ivar

Hi,


Why not feed a PDE on the boundary of the pipe instead. The PDE for the boundary would then take care of the nano-scale physics.

We don't work on nano-scale problems here, but we have a similar issues when we want to model flow and transport cracks through a domain whose sizes are significantly smaller than that of the domain, for instance the embedded cracks we model are just 300 micro meter, and the domain is about 2 m. So cracks are represented as internal boundaries with convection-diffusion equation defined and properties that are unique to the cracks. In this way, we don't bother with discretising the thickness of cracks. Of course finer discretisations would be necessary close to the crack surface to get more accurate solutions, but not to the level if you would really represent a nano-scale domain. We also have problems in which flow occurs around the wall of a porous block whose velocity is several orders of magnitude higher than that of the porous matrix, for which we take the same approach.

You can see an example available in the subsurface module called "discrete-fracture".

I am not sure if this helps you.


Suresh

Hi,


Why not feed a PDE on the boundary of the pipe instead. The PDE for the boundary would then take care of the nano-scale physics.

We don't work on nano-scale problems here, but we have a similar issues when we want to model flow and transport cracks through a domain whose sizes are significantly smaller than that of the domain, for instance the embedded cracks we model are just 300 micro meter, and the domain is about 2 m. So cracks are represented as internal boundaries with convection-diffusion equation defined and properties that are unique to the cracks. In this way, we don't bother with discretising the thickness of cracks. Of course finer discretisations would be necessary close to the crack surface to get more accurate solutions, but not to the level if you would really represent a nano-scale domain. We also have problems in which flow occurs around the wall of a porous block whose velocity is several orders of magnitude higher than that of the porous matrix, for which we take the same approach.

You can see an example available in the subsurface module called "discrete-fracture".

I am not sure if this helps you.


Suresh

Hi,

Thanks for your reply.
But actually we want to track the effect of the processes that are unique to the nano-scale region. So if I give a pde which represents the transport process inside the nanoregion as the b.c. at the boundary of microscale region, I will not be able to track what is happening in the nano-scale region. Hope I am correct.
If possible,can you please have a look at the model mesh.mph which I have attached in this thread . Is this kind of meshing acceptable?

Regards,
Seetha

Hi,


I must admit that I have not used identity pairs in any of my problems although long time ago I did some tricks in version 3.5a to map primary variables across the domains. So please treat my crude answer here with caution.

If I am right your concern is that at the mesh interfaces the vertices do not necessarily match? But I think this is how it would be when you have the provision of identity pairs. I just opened thin layer diffusion application in the model library to see whether they have a similar situation with the meshing because they also use identity pairs in matching two 3D domains. So I guess COMSOL is capable of handling such discretisations.

I don't work in your area, but typically, we don't mix nano-scale behaviour with continuum scale simply because the latter is an averaged behaviour - of course this is the case mainly in heterogeneous materials. Your case is not of heterogeneity, so I presume that the physics of nano-scale you are feeding into the domain closest to the wall is different from that of the continuum scale. Any way just a thought.

As Ivar kindly pointed out that you definitely have to check for both spatial and temporal convergence, this is our experience especially when discrete cracks were represented as internal boundaries. In general, I always got good convergence using mapped linear elements rather than mapped quadratic elements, don't know why.

More importantly, if at all you were to use stabilization techniques, I have certainly no idea on the effect of smoothing on your results especially in the nano-scale region or at its interface where you want to capture processes rather accurately.


Suresh

Hi
Thanks for your reply. The physics in the nano-scale region is different from that in the continuum scale. My concern is some of the nodes at the interfaces are matching. But many nodes of the nano-scale region at the interface exist between two nodes of the continuum-scale region at the interface. Hope I am able to convey my doubt properly.
But as Ivar said, if COMSOL is capable of interpolating the fluxes from the continuum-scale elements to the nodes of the nano-scale region at the interface, then it will be fine.

Regards,
Seetha

Hi

that is certainly one way, you mightconsider a geometric progression with an Element ratio greater than 1 to have an increasing mesh dimension to the next step (perhaps 10 or even 100, try)

Now I cannot say it it's OK or not because that would depend on the model and the gradients you have.
plot the gradient along a cut line on a log scale with a marker on the data points (mesh) and estimate howyour gradient is resolved. If the gradient is nicely axisymmetric probbaly it should do, the best is to double (or half) the esh density and see how the solution evolves, if greatly different (typically >5-10%) probably you should even make a denser mesh

--
Good luck
Ivar

Hi

I believe there is no "one answer", if I have such large scale difference I make aften my domains with interiour boundaries such that I mesh the regions with different densities. Often I use boundary mesh elements with very uneven shapes, but this depends on the model.

Basically the mesh is a "sampling" of your equations, if these have a very steep gradient along Y and a small gradient along Y, you can use safely a elongated mesh, long along Y and very short along X.

The average mesh quality is for homogenious or isotropic mesh cases, a COMSOL mesh quality of 1e-5 can be perfectly OK for a highly anisotropic case provided that the linear mesh quality is respected along the different directions.

One way to check your results is to solve for mesh density of 1 and then of 2 (or 0.5) and look at the resultes, by how much do they change

When I talk about sampling, it is not only spatial sampling, but also transient, particularly in diffusion equation cases with step wise boundary conditions (often along constant temperature T or concentration C boundaries, for the rest of the environment at "0" initial conditions

For the oscillations, check the Reference guide about stabilization techniques

--
Good luck
Ivar

Hi

you can add different mesh nodes, and add for each a mesh Size sub node and define in several steps, convert your default "physics induced" mesh into a user mesh (check the doc, its worth to read it carefully, I agree it takes some time but there are so much to learn in the beginning, the only way is to start ;)

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Good luck
Ivar