25 Jan 4 Mesh issues causing poor CFD simulation accuracy
As strange as it sounds, often the most critical part of a CFD simulation cycle (from geometry preparation to result analysis) is not the solution of partial differential equations. Instead, the real added value of a good CFD software is represented by meshing capabilities, automation, robustness and quality assurance. The (seemingly) “simple” task of dividing a given space in small control volumes is full of geometrical problems, singularities and tricks hard to deal with.
In addition to the complexity it presents, a good meshing is fundamental in order to obtain meaningful and reliable CFD results. Before running any CFD analysis, to check the mesh quality is a must.
In this post are presented the four most common aspects the user has to keep an eye on when evaluating a mesh quality.
DEFINITION: The “speed” the cells volume changes from the maximum to the minimum value (or vice versa).
The slower it changes the higher the uniformity, the better the accuracy.
This aspect is strictly related with the so called “grid refinement” (for an explanation of common CFD terms, take a look at this post). In general, the best accuracy is obtained when using cells of the same dimension in the whole domain. In some zones of the flow the maximum dimension allowed is very small (find out why in this post). So that, having all cells of this very small volume cannot be achieved for most industrial applications, as it would lead to grids with too many cells to be handled, resulting in a too high computational burden.
Having this constrain in mind, during meshing phase the analyst (or the software A.I.) has to choose where cells can be enlarged, limiting the number of total cells while maintaining a good resolution in critical zones. It is at this point that the mesh uniformity comes into play, and it has to be carefully taken into account to obtain meaningful and accurate results.
BEST: Zero volume variation, maximum uniformity
WORSE: Steep volume variation, low uniformity
DEFINITION (general 3D cases): It is the maximum value between
- The ratio between the maximum and the minimum area of the cell’s bounding box
- The following expression 1/6 * ( |ax| + |ay| + |az| ) / (V ^ (2/3))
- where ax, ay, az are the areas of the cell’s bounding box
- V is the cell’s volume
The closer to 1.0, the better the accuracy.
This particular mesh feature is encountered especially when dealing with boundary layer and anisotropic refinement for hexahedral-dominant meshes. The former case consists of meshes that have very stretched cells in the near wall region to capture near wall flow behavior.
The latter can be found in castellated meshes (typically encountered in very simple and approximated solver technologies such as immersed boundary) when one wants to limit the number of cells in one direction while maintaining a prescribed resolution in the orthogonal one (i.e. in case of atmospheric simulations when the refinement in the zenith direction is prescribed while the “in plane” spacing can be coarsened).
BEST: Aspect ratio = 1
WORSE: Aspect ratio = 16
DEFINITION: The angle between the line connecting two cell centers and the normal of the face they share.
The closer to 0.0, the better the accuracy.
This aspect often shows up in polyhedral meshes, where the cells shape can vary a lot in a confined space. It has a strong impact on simulation accuracy, since it is closely related with variable gradients and viscous and convective fluxes calculation.
The solver of our Cloud CFD is based on the OPENFOAM® library, so that we take advantage of all the available countermeasures to assure a proper correction to this mesh problem and to provide our users with accurate and reliable results.
BEST: Orthogonality angle = 0 deg
WORSE: Orthogonality angle = 45 deg
DEFINITION: The distance between the intersection of the line connecting two cell centers with their common face and the center of that face.
The closer to 0.0, the better the accuracy.
A combination of complex geometries with too coarse meshes often results in too large values of skewness. As for the previous issue, this as a strong impact on results accuracy, and again it influences the flux balance calculation.
To improve this specific mesh quality criteria it is usually successful to increase mesh resolution in zones where the geometry has complex features and to increase mesh uniformity.
BEST: Skewness = 0
WORSE: Skewness = 0.25
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