Quality Checks (PART I)

 Hey Guys,

Today we are discussing an important topic which is, How we can check our mesh?

Is it right? according to the ideal shape? and how can I correct it if it is not? Firstly understand that this Quality check has two parts in which are Part I and Part II will be posted very soon. 

So, now let's understand why quality checks?

When we carry the meshing for a complex geometry our mesh is get distorted from its ideal shape.

Every element is designed to work properly within a certain range of shapes of distortion. Exactly how much distortion it depends on is get known to us by the quality check of mesh. 

        The Ideal shape for a Triangular element is an Equilateral triangle and for that of quad elements, it is square. And for the tetrahedron element is a regular or isosceles tetrahedron and for Hexahydron it is a cube. When we assume the actual shape or ideal shape of our mesh and place it in the model, the shape may differ from its natural shape this is because it is not possible to map the exact shape of mesh to the geometry due to geometry shape. 

Thus we can't make accurate or actual shape mesh to the geometry but we can try to achieve this. So this can be done by the quality parameters which is given below:

1. Skewness

2. Aspect Ratio

3.Included angles

4. Jacobian

5. Stretch etc.

These are the measures of how far can a given element derivate from its ideal shape.

Note that some of the quality parameters are based on angles like (Skew) while others on side ratio like (Aspect, Stretch, etc)

To reduce solution time element is mapped to the local coordinate system. Instead using a global coordinate system. The effectiveness of this is checked by the Jacobian and distortion.

 What we expect that all nodes should lie in the same plane but this is an ideal situation or for a cube but in curvatures, it is not possible to do so. 

So when the angle goes out from the expected angle it is known as the wrap angle.

1. Wrap angle: 

The wrap angle is out of the plane angle.

The ideal value is 0 degrees acceptable is <10 degree

Not applicable for triangular elements. 

Define as it is the angle between two normal planes formed by splitting quad elements.

2. Aspect: 

Aspect is max. element length edge length to the minimum element length.

Ideal value = 1 acceptable < 5

3. Skewness: 

Skewness is the Angular Measure of Element quality with respect to the Angles of Ideal Element Types. And it determines how close to ideal a cell or face is.

Ideal value = 0 Acceptable < 45 degress.

4. Included angle:

Skew is based on the overall shape of elements it does not take into account individual angles.  

Quad Ideal value = 90 degress Acceptable 45 <Q<135

Tria ideal value = 60 degrees  Acceptable 20<Q<120

5. Jacobian: 

what is jacobian in simple language the jacobian is a scale factor arising because of a transformation of the coordinate system. Elements are transformed from global coordinate to local coordinate.

Ideal value 1.0 Acceptable >0.6

6. Stretch:

In simple language, the stretch is the stretching of the element length from one side.

Ideal value 1.0 Acceptable >0.2

For quad element stretch = Lmin*Root12/dmax.

For tria element stretch = R*Root12/Lmax.

Part-II of the blog will come soon in which we are going to discuss "How to improve quality of poor elements" So stay tuned.

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