### How does FEniCS handle 2D models?

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Dear FEniCS community,

In the problem I am trying to solve, there are intensive properties such as the volumetric heat capacity (units: J / cm3 / K). This would be fine and dandy if I was implementing a 3D model, but I am aiming for a 2D model, since it is less computation intensive, and should conceptually yield a meaningful answer. Just by the look of it, I have a dimensionality mismatch with the units that I need to correct if the results shall mean anything.

Now, how does FEniCS actually handle 2D models? Does it create a slab of finite, but very small, thickness or is it purely 2D?

In the latter case, I would expect that I need to convert my volume-dependent properties to area. Are there established methods to do so?

Many thanks for your time. I am looking forward to your answers.

In the problem I am trying to solve, there are intensive properties such as the volumetric heat capacity (units: J / cm3 / K). This would be fine and dandy if I was implementing a 3D model, but I am aiming for a 2D model, since it is less computation intensive, and should conceptually yield a meaningful answer. Just by the look of it, I have a dimensionality mismatch with the units that I need to correct if the results shall mean anything.

Now, how does FEniCS actually handle 2D models? Does it create a slab of finite, but very small, thickness or is it purely 2D?

In the latter case, I would expect that I need to convert my volume-dependent properties to area. Are there established methods to do so?

Many thanks for your time. I am looking forward to your answers.

Community: FEniCS Project

### 1 Answer

4

*>"Now, how does FEniCS actually handle 2D models? Does it create a slab of finite, but very small, thickness or is it purely 2D?"*

Of course not... it does not create a thin layer. If you start with a mesh, say UnitSquareMesh, you have purely 2D domain.

Dimensional reduction is often a difficult question and has nothing to do with FEniCS. The answer to that depends on specific problem that you would like to solve.

Just imagine an experiment of heat propagation in a cube. When you do a slice of it (and compute something in 2D fenics model) you wont get reasonable answer, because you do not see propagation in direction perpendicular to this slice. You must reduce the original 3D model to 2D/1D model assuming some symmetry in the problem (there is a coordinate in the system, such that the solution doesn't depend on this coordinate).

written
5 months ago by
François Lapointe

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