Depending on the robustness of the solver, every commercial cfd software are limited to an maximum skewness or for that matter aspect ratio that they can support; for eg a skewness of 0.98 to 0.99 in case of FLUENT. I would like to know what would be the issue with highly skewed cell, how a highly skewed cell causes convergence issues.
Hello, Mr. Alayil,
In the finite volume method, all equations are discretized using the distance between the centroids of adjacent cells, with the assumption that the vector joining these centroids is perpendicular to the common face. (See Fig A).
However, when this criterion is not satisfied, i.e., when the centroid-to-centroid vector is not normal to the face (Fig B), the flux that is being calculated is no longer normal to the face, and leads to erroneous values of variables in the control volume. This is what prevents convergence, and sometimes also causes the solution to diverge.
The distance between p1 and p2 is used to calculate skewness.
I have used PHOENICS with extreme aspect ratios and there was no convergence problem! There is of course an ACCURACY problem bdecause of the way these codes do the averaging (linear or harmonic)
@ Markatos, thanks for your time. Can you give me a better insight or some documents that would help me.
Unfortunately no documents, only experience. I suggest you make runs with different aspect ratios and gain insight. Of course if u use explicit techniques ( for which I say keep away ) then you have limitations on grid size/time step.
Hello, Mr. Alayil,
In the finite volume method, all equations are discretized using the distance between the centroids of adjacent cells, with the assumption that the vector joining these centroids is perpendicular to the common face. (See Fig A).
However, when this criterion is not satisfied, i.e., when the centroid-to-centroid vector is not normal to the face (Fig B), the flux that is being calculated is no longer normal to the face, and leads to erroneous values of variables in the control volume. This is what prevents convergence, and sometimes also causes the solution to diverge.
The distance between p1 and p2 is used to calculate skewness.
Depending on the equations you are solving, and the numerical method you use, you can have the aforementioned effect of computing non-normal fluxes across cell edges together with a second effect which comes from the ratio of length to area of the cell. This can be sensitive using explicit solvers. Very skewed triangular cells, that is, cells with their smaller internal angle being very small, tend to a line instead of a triangle. Depending on the way that stability is ensured in the numerical scheme, the basic assumptions that are kept for stability may not be satisfied.
In my experience, if you have both effects, the latter can be very destructive, effectively producing unstable solutions. The first, on the other hand, in my experience, provided inaccurate solutions, but no instabilities.
Dr Daniel,
Thank you for differentiating between instability and inaccuracy - I suppose non-extreme skewness leans to the latter.
This also makes non-extreme skewness a stealthy threat that is hard to detect. Since the solution is converging, it would be difficult to determine its correctness in the absence of another reference for cross-checking. Would you recommend a metric to judge whether skewness is within 'acceptable' levels? I could never really determine the reason behind the 0.98 skewness limit in Fluent.
I don't think that there is a general rule. It depends heavily on the equations, and the discretization approach. Explicit, first order methods, I think, would be more sensitive, since stability can be easily compromised. In my experience, strong hyperbolic properties in equations make the solution more sensitive to both. Stability of course, (since the system may be very demanding in such sense) but also in inaccuracy derived from non-normal fluxes. Parabolic equations, in my experience, seem less prone. But, as I say, I think this is only a conceptual guideline. To really assess the impact, it is important to understand stability properties of the scheme, and of course, simply test and see what happens.
Rajesh Alayil The highly skewed cell mostly causes ill conditioning effects during function approximations in a numerical method, such as the local second-order or high-order reconstruction, node collinear in least square, linear system, negative elemental Jacobian mapping..., and these all can be attributed to the ill conditioning caused by geometric stiffness(e.g. skewed cell)
@Hiro There are several papers mentioned separately the mentioned issues are caused by the existence of skewed elements, but I cannot remember the paper's titles...
Here is a reference, that may help in studying anisotropy of grid/ cell in computing:
Article Analysis of anisotropy of numerical wave solutions by high a...
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