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Grid refinement ratio for unstructured mesh

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Old   February 28, 2013, 12:19
Default Grid refinement ratio for unstructured mesh
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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 r for unstructured meshes, using their element-counts N_1 and N_2:

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 11:18. Reason: Correction in formula of r
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Old   March 4, 2013, 05:10
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D = 1 for a one-dimensional case.
D = 2 for a two-dimensional case.
D = 3 for a three-dimensional case.
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Old   March 4, 2013, 05:17
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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...
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Old   March 4, 2013, 11:15
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typo in post #1, r formula is r=\left(\frac{N_1}{N_2}\right)^{1/D}
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Old   March 4, 2013, 11:18
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macfly, thanks. Corrected.
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