[Steve1999]

Dear all,

I am new to cfdonline and solids4foam. I noticed that there are two solid models available in solidModels in solids4foam: linGeomTotalDispSolid and unsLinGeomSolid. Upon comparing their C and H files, I observed that the latter includes an additional operation, correct(sigmaf_). Although the description provides a brief overview, I would appreciate a more detailed explanation. Could anyone please elaborate on the algorithmic differences between these two solid models and the reasoning behind their design? What are the typical use cases for each model? Are there any specific scenarios where one is preferred over the other?

Additionally, are there any relevant literature or references that anyone could recommend for further reading on the unsLinGeomSolid model? I would greatly appreciate any guidance that someone can offer.

PS: Can I incorporate the correct(sigmaf_) function into linGeomSolid?

Best,
Steve

[bigphil]

Hi Steve,

The difference between linGeomTotalDispSolid and unsLinGeomSolid is how they calculate the displacement gradient at the cell faces.

In linGeomTotalDispSolid, the displacement gradient is calculated at the cell-centres and interpolated to the faces. The resulting discretisation is unstable and a Rhie-Chow diffusion stabilisation term is added to the momentum equation to resolve this.

In unsLinGeomSolid, the displacement gradient is calculated directly at the faces, where the normal component is calculated using a compact molecule (owner and neighbour values) and the tangential gradient is calculated using the Gauss method on the face and the vertex displacement values. The vertex displacement values are calculated by interpolating from the cell centres using a least squares method.
The resulting discretisation is stable and does not need additional stabilisation like Rhie-Chow, although it can be added if desired.
The "uns" prefix comes from "unstructured", as the method was initially created (by Zeljko Tukovic, Zagreb) with the goal of being more accurate on unstructured meshes.

In terms of their relative merits, unsLinGeomSolid is more accurate than linGeomTotalDispSolid. Also, unsLinGeomSolid should provide second-order accuracy for the maximum and average discretisation errors in displacement and stress, whereas linGeomTotalDispSolid is likely only second-order for the average stress errors.
However, unsLinGeomSolid is approximately twice as slow as linGeomTotalDispSolid, primarily due to the cell-to-point interpolation. In addition, they may display different parallel scaling behaviour.

[Steve1999]

Hi Philip,

Thank you for your detailed response. I was wondering if it's possible to learn the relevant theoretical knowledge through literature and books. For example, the work by Zeljko Tukovic that you mentioned. Do you have any recommendations?I'm quite interested in this topic, and I'd like to dive deeper.

Additionally, I've noticed that for some problems, using an incremental unknown solidmodel, such as linGeomSolid, seems to yield better results. Would it make sense to add the correct(sigmaf_) function to linGeomSolid?

[bigphil]

The unsLinGeomSolid solver is described in https://hrcak.srce.hr/206941.

Sure, if you like, you can create an incremental version of unsLinGeomSolid (i.e., solve for DD instead of D). Before that, you may like to try enabling the "predictor" option, which may give the same behaviour as an incremental version because the displacement field is predicted as the start of each time step using the velocity.

[Steve1999]

Hi Philip

Thanks for your suggestion. I'll try out the predictor you mentioned first and then compare the result with linGeom.

Best,
Steve