CFD and corners
 

Hi everyone,

I have a very stupid question so I guess somebody could answer it easily. Why CFD gives bad results when it´s applied over corners? My teacher always told me that if the geometry has very marked corners then probably CFD will not provide accurate results, but why?
And why CFd provides bad results when cells have high skewness or aspect ratios?

Thanks in advance, I am a beginner...

It's not very clear to me what your teacher says: I could imagine that main problems could be related to:
- mesh, as you wrote: skewness
- flow separation in turbulence regime: but there are some specific models to predict separation.

Daniele

Hi Daniele,

Thanks for the reply, but you have not answered my question. Why a CFD code(for example FLUENT or OpenFOAM) provides bad results (or even do not achieve convergence) when the geometry have very marked corners? Is it due to numerical schemes (finite volume method) or is it a problem related to conservation equations? Or perharps is it due to the meshing produced to discretize this corner (skewed elements)?

Thanks

The statement that codes give bad results at corners is an overly general one, and as ghost82 pointed out, there are a number of possiblities why such problems may occur. That would depend on the scheme, the way the BCs are enforced, the type of equation solved, the flow situation, the meshing etc...

It is a very broad statement and not true in general, so it is difficult to answer what your prof had in mind.

More often than not, domain corners imply some form of singularity which, for example, has to be carefully treated in higher order methods in order to mantain the expected order of convergence (e.g., spectral methods).

Mesh skewness is a totally separate issue, which might be present or not near a domain corner. Very roughly speaking, in FV the issue for the skewness and mesh non orthogonality in general is related to the alignment of face normals and face centroids with respect to the cell centers.

One more reason can be fluent,etc, solver is based on cell centred calculation, which then is extrapolated on the corner. This would be depending on the Mesh size at the corner points.

It is a problem due to singularity appearing in the representation of the continuous geometry over a discrete mesh representation.

Thank you. I have not come across singularity problem in CFD much. Is singularity related to zero volume cells which gets created while generating mesh.

The singularity is related to the fact that you are fixing your solution over a non regular boundary. The consequence is that some derivatives of the solution might not exist (which might become an issue for high order methods).

The issue is described, for example, in Boyd: Chebyshev and Fourier Spectral Methods, Chapter 19. However, nearly all the books on spectral methods have at least a small description of this issue.

Hi Tensian,

First, good on you for posting your very excellent question and trying to understand the ins and outs of what your professor has been teaching/telling you.

As pointed out in some of the responses, your question is stated in very general terms and would benefit from being more specific. As a counter-example, sharp corners in bluff body are well defined separation points which are easier to predict in CFD.

Below may be an explanation of what your teacher may be referring to:

Fluent and openFoam are general purpose CFD software using the finite volume method. As you may be aware, the finite volume method solves the variable at the cell center, and uses projection of the variable to the faces to calculate the flux used in the conservation equation.

Typically boundary layer meshes are applied near walls, resulting in cells with large aspect ratio (thin, but long and large). At sharp corners, the mesh would look as follows (depending on what software you may be using):

https://dl.dropboxusercontent.com/u/...e-10102013.png

In such case, non-orthogonality issues associated with the face (shown in red) and interpolation of the cell centered variable to the face can be problematic.

No pictures shown
 

hi...thanks for your good reply....But The pictures not available...
if it's possible for you upload it again....Thank you