[Gerry Kan]

Howdy Folks:

I am considering two methods of handling geometries that cannot be mapped using conformal methods (think buildings protruding from the ground):

1. Unstructured grid - geometries become physical boundaries
2. Immersed boundary method (IBM) - boundary grid points immersed in a Cartesian grid

For those who worked with IBM, would you recommend this method over the unstructured grid approach. I understand that IBM has been used for FSI, but in this case I am not expecting the "structure" to be in motion in any way. Would it still make sense?

If you could also recommend some references or papers, this will help give a more well-rounded opinion on this.

Thank you very much in advance,
Gerry.

[sbaffini]

If it is (easily) doable (and from your geometries it seems quite so to me), always stick to body fitted grids (unstructured or not).

There are a bazillion kind of possible approaches to the immersed boundary, but each one of them has its own limitations with respect to the classical body fitted approach. Unfortunately, every single paper on immersed boundary methods concludes that the proposed method solves the underlying problems, while a more accurate statement would mention the acknowledged problems instead.

One such problems, for example, is linked to the fact that the convective fluxes at walls are not exactly zero anymore, but subject to the interpolation error (roughly speaking, as you don't have anymore a real grid boundary where you know the flux is zero, you put a non zero value somewhere else, but it is not exact anymore and, by themselves, they don't even sum up exactly to zero without some correction).

The main use case for the immersed boundary is, in my opinion, difficult/impossible meshes and moving bodies. Your case doesn't seem to fit any of them.

Note that I currently develop an immersed boundary code with underlying unstructured grids, I would promote it if it was suitable.

Of course, there is always a third use case, which is: I don't want to make the mesh. Legit, then go immersed boundary, but the specific code that you use has huge relevance.

[FMDenaro]

Originally Posted by Gerry Kan

Howdy Folks:

I am considering two methods of handling geometries that cannot be mapped using conformal methods (think buildings protruding from the ground):

1. Unstructured grid - geometries become physical boundaries
2. Immersed boundary method (IBM) - boundary grid points immersed in a Cartesian grid

For those who worked with IBM, would you recommend this method over the unstructured grid approach. I understand that IBM has been used for FSI, but in this case I am not expecting the "structure" to be in motion in any way. Would it still make sense?

If you could also recommend some references or papers, this will help give a more well-rounded opinion on this.

Thank you very much in advance,
Gerry.

My opinion is that one should use always an unstructured grid ... at least until that is possible.
Have a look to this review https://www.annualreviews.org/doi/ab....061903.175743

[Gerry Kan]

Gentlemen:

Thanks for your feedback. Fillipo, I read the Iaccarino paper you sent me, and it was insightful.

I am drawing parallels between IBM and cut-cell methods, something I am familiar with, and probably they share the same advantages and drawbacks.

Gerry.

[sbaffini]

Originally Posted by Gerry Kan

Gentlemen:

Thanks for your feedback. Fillipo, I read the Iaccarino paper you sent me, and it was insightful.

I am drawing parallels between IBM and cut-cell methods, something I am familiar with, and probably they share the same advantages and drawbacks.

Gerry.

In general, the cut-cell approach is by someone considered an immersed boundary approach. But it really depends from the implementation as well.

If the output of the underlying cut-cell algorithm is a grid which is exactly cut by the geometry (altough automatically) and each boundary exactly follows the underlying geometry, does it make any sense to still call it an immersed boundary approach? Maybe it is just automated meshing, which is indeed cooler, because you have none of the problems I mentioned, but it is not immersed boundary anymore.

Still, I acknowledge that there are implementations that, at some point in the cut-cell process, make further simplifications in order to gain robustness, speed, or whatever. The output may still be an unstructured body fitted grid, but probably not as accurate as one might expect. Probably, in this case, it might have more sense to call them immersed boundary. Still, I would find this terminology extremely confusing for novices.

[FMDenaro]

Originally Posted by Gerry Kan

Gentlemen:

Thanks for your feedback. Fillipo, I read the Iaccarino paper you sent me, and it was insightful.

I am drawing parallels between IBM and cut-cell methods, something I am familiar with, and probably they share the same advantages and drawbacks.

Gerry.

Yes, the IBM method for a fixed rigid geometry is very similar to the cut-cell method

[Gerry Kan]

Gentlemen:

Okay, thank you for your input. In this context I should be able to decide what to do next while giving a fairly balanced argument on both sides, at least for the application I am considering.

Gerry.

[FMDenaro]

I can also suggest to follow the lectures of C. Peskin next month and the material of his course


https://math.nyu.edu/dynamic/courses...-descriptions/


https://www.math.nyu.edu/faculty/pes...tes/index.html

[aerosayan]

Dear Gerry,


I'm sure many of the experts have already given great information on the advantages of IBM.
IBM is a really powerful method after all.


I will share why one disadvantage because of which I didn't use it.


IBM require a lot of cells to represent the boundary (See AMR_regridding.jpg). Most of that computational power could have been spent on actually resolving the turbulence, shocks and doing faster iterations. IBM didn't seem suitable to me for flows where the body could be represented in the form of multiple structured blocks, and we could adaptively refine those grids(See cfl3d-grid.gif).


It takes a little extra effort to first generate the base grid, but the code is flexible to work on any kind of domain that can be represented as a patch of multiple structured blocks.


Thanks and regards
~sayan

[sbaffini]

Originally Posted by aerosayan

Dear Gerry,


I'm sure many of the experts have already given great information on the advantages of IBM.
IBM is a really powerful method after all.


I will share why one disadvantage because of which I didn't use it.


IBM require a lot of cells to represent the boundary (See AMR_regridding.jpg). Most of that computational power could have been spent on actually resolving the turbulence, shocks and doing faster iterations. IBM didn't seem suitable to me for flows where the body could be represented in the form of multiple structured blocks, and we could adaptively refine those grids(See cfl3d-grid.gif).


It takes a little extra effort to first generate the base grid, but the code is flexible to work on any kind of domain that can be represented as a patch of multiple structured blocks.


Thanks and regards
~sayan

Not exactly true. Anisotropic cartesian grids can, indeed, be sufficiently efficient in describing geometries. Probably not as much as the body fitted counterpart but they can easily recover in transitioning to coarse zones away from boundaries. Look, for example, at the 2^N tree as developed by Prof. Z.J. Wang during his years at CFD Research.

[andy_]

Originally Posted by Gerry Kan

For those who worked with IBM, would you recommend this method over the unstructured grid approach. I understand that IBM has been used for FSI, but in this case I am not expecting the "structure" to be in motion in any way. Would it still make sense?

It depends on the type of problem you are solving. In the late 70s and early 80s I joined a CFD group developing methods using Cartesian grids in a castellated form and cut cell form. This was before the explosion in finding a name for every conceivable variation in a set of assumptions and so I must confess to not knowing the current labels. My role was to help develop a body fitted method but I used the Cartesian grid methods in comparisons.

The Cartesian grid methods performed poorly with boundary layers over curved aerodynamic surfaces. If you castellated the geometry then a diffusing flow would separate much too early. If you cut the cells then a correction based on geometry applied to the mass fluxes (proportional to u) and momentum fluxes (proportional to u^2) created strong compensating local pressure gradients in the cut cells leading to spurious local flow. I am fairly confident the strength of the "noise" in the cut cells could have been reduced by dropping the notion of a precise geometric boundary and smearing/smoothing the flux corrections. Although a reasonable assumption for walls that are not the main factor in driving the flow it is not for boundary layers over aerodynamic surfaces. The boundary fitted grid proved sufficiently superior for this type of flow region that development of the Cartesian grid methods largely ceased except for some initial model development due to simpler terms in the equations.

Perhaps I should add that variations of this type of approach were retained in modelling premixed flames using what we at the time called the g equation and which later become known as the level set method.

If you are modelling individual buildings then a Cartesian grid approach is unlikely to be optimum but if you are modelling towns or cities where individual buildings cannot be adequately resolved then it may be the optimum approach subject to sorting out the empiricism.

[aerosayan]

Originally Posted by sbaffini

Not exactly true. Anisotropic cartesian grids can, indeed, be sufficiently efficient in describing geometries. Probably not as much as the body fitted counterpart but they can easily recover in transitioning to coarse zones away from boundaries. Look, for example, at the 2^N tree as developed by Prof. Z.J. Wang during his years at CFD Research.

If the boundary is being represented with aniostorpic cells, are you translating/rotating the cells to align with the flow direction and the curvature of the body wall?


The idea is really nice, can be useful in 3D.

[sbaffini]

Originally Posted by aerosayan

If the boundary is being represented with aniostorpic cells, are you translating/rotating the cells to align with the flow direction and the curvature of the body wall?


The idea is really nice, can be useful in 3D.

Not in my case, but that is roughly what cartesian body fitted grid generators do near boundaries. Besides the papers by Wang there is also a thesis from a former phd student of hirsch that describes what is, probably, the core of hexpress by numeca