Grid refinement ratio for unstructured mesh
 

Hello,

I am trying to streamline the mesh independence practices using Grid Convergence Index and Richardson Extrapolation as they are considered the best in practical CFD. (Ref: Roache, P. J. "Perspective: a method for uniform reporting of grid refinement studies." TRANSACTIONS-AMERICAN SOCIETY OF MECHANICAL ENGINEERS JOURNAL OF FLUIDS ENGINEERING 116 (1994): 405-405.)

Now, element sizes for the consecutive meshes should be known to get the grid refinement ratio used in the calculations in this procedure. But since we use unstructured mesh along with the extruded mesh; I am not sure if the value of element local element size (in the important regions of high gradients) is representative of the size for that particular mesh.

Roache suggests the following formula for grid refinement ratio for unstructured meshes, using their element-counts and :



Now, he defines D as Dimensionality. What does it mean and how to calculate it from the fluid domain?? :confused:

Thanks
OJ

D = 1 for a one-dimensional case.
D = 2 for a two-dimensional case.
D = 3 for a three-dimensional case.
:cool:

The idea behind it is that if you want cells with half the edge length in a 3D domain, you need 2^3 times as many cells...

typo in post #1, r formula is

macfly, thanks. Corrected.