Grid refinement ratio for unstructured mesh

oj.bulmer · February 28, 2013, 11:19

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

:

$r = \left(\frac{N_1}{N_2}\right)^{1/D}$

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

Thanks
OJ

RodriguezFatz · March 4, 2013, 04:10

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

flotus1 · March 4, 2013, 04:17

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...

macfly · March 4, 2013, 10:15

typo in post #1, r formula is $r=\left(\frac{N_1}{N_2}\right)^{1/D}$

oj.bulmer · March 4, 2013, 10:18

macfly, thanks. Corrected.

February 28, 2013, 11:19	Grid refinement ratio for unstructured mesh	#1
oj.bulmer Senior Member OJ Join Date: Apr 2012 Location: United Kindom Posts: 473 Rep Power: 20	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 : $r = \left(\frac{N_1}{N_2}\right)^{1/D}$ Now, he defines D as Dimensionality. What does it mean and how to calculate it from the fluid domain?? Thanks OJ Last edited by oj.bulmer; March 4, 2013 at 10:18. Reason: Correction in formula of r

March 4, 2013, 04:10		#2
RodriguezFatz Senior Member Philipp Join Date: Jun 2011 Location: Germany Posts: 1,297 Rep Power: 26	D = 1 for a one-dimensional case. D = 2 for a two-dimensional case. D = 3 for a three-dimensional case. __________________ The skeleton ran out of shampoo in the shower.

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March 4, 2013, 04:17		#3
flotus1 Super Moderator Alex Join Date: Jun 2012 Location: Germany Posts: 3,399 Rep Power: 46	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...

March 4, 2013, 10:15		#4
macfly Senior Member François Grégoire Join Date: Jan 2010 Location: Canada Posts: 392 Rep Power: 17	typo in post #1, r formula is $r=\left(\frac{N_1}{N_2}\right)^{1/D}$

March 4, 2013, 10:18		#5
oj.bulmer Senior Member OJ Join Date: Apr 2012 Location: United Kindom Posts: 473 Rep Power: 20	macfly, thanks. Corrected.