Short Story: The Truth Surrounding MESHES

The results of Computational Fluid Dynamics is mainly governed by two parameters:
1)Meshing
2)Post-processing

The meshing affects the accuracy and the stability of the CFD solution to a large extent.

To begin with, CFD meshes are primarily of two types:
1)Structured Mesh
2)Unstructured Mesh
Structured mesh is made up of regular mesh cells and the pattern repeats itself throughout whereas Unstructured mesh is more versatile and can comprise cells of different shapes and sizes and the pattern may be irregular.

Now, the quality of the mesh cells is governed by 4 primary metrics:
1)Aspect Ratio
2)Jacobian Matrix
3)Non-orthogonality
4)Equiangular Skew

Aspect Ratio may be defined as the ratio of the longest side to the shortest side.
Different CFD solvers calculate the aspect ratio in different ways and it’s quite complex when we consider non-regular polyhedra.
For example, ANSYS Fluent calculates the distance of various nodes from the centroid, and then it calculates the ratio of the longest of this distance to the shortest of this distance.
Whereas OpenFoam calculates via the ratio of the longest side to the shortest side.
We get a stable CFD ratio if the aspect ratio is greater than 1000 and a very accurate solution if it is less than 10.

Jacobian Matrix talks about the inverted mesh cell, if a cell is inverted it has a jacobian value less than 0. A preferred Jacobian value is 0.2 or greater.

Non-orthogonality is we draw a vector that is out of the cell face and then we see if we can decompose it into two other vectors which are orthogonal to each other.

Equiangular skew talks about whether the regularness of the polygon. The interior angle of a regular polygon is estimated via the formula((180*(N-2))/N), where N represents the number of faces of the polygon.

The mesh quality metrics can be classified as:
1)Cell metrics which includes Aspect Ratio and Jacobian Matrix
2)Face metrics which includes Non-orthogonality and Equiangular skew

It is important to have a good quality mesh before it is involved in the CFD solver for its solution to converge. If the mesh quality is of poor quality then the CFD solution would diverge.
CFD solutions could be derived from the summation method or inversion of the matrix method( AT=B; Ais the coefficient matrix; T is the matrix of variables; B is the matrix of unknowns)

With every iteration in the CFD process, non-orthogonality terms are introduced and the solution finally converges. If we have a mesh comprising of skewed cells more terms have to be introduced and it takes a long term to converge.

Hope via this blog I justified the importance of Meshes in CFD :)