Why should HEX20 elements be used instead of HEX8 elements?

[MWTWM M]

Dear community,

 

In cases without curved boundaries, what advantages does a HEX20 mesh offer compared with a HEX8 mesh? In cases involving curved boundaries, if one still intends to use a HEX20 mesh, how should lx1 and lxd be configured to ensure sufficient accuracy?

 

Any suggestions and criticisms are appreciated.

Student W. T. Ma

[YuHsiang Lan]

Hi,

In short,

> In cases without curved boundaries, what advantages does a HEX20 mesh offer compared with a HEX8 mesh?

   No advantages.

> how should lx1 and lxd be configured to ensure sufficient accuracy?

   lx1 >= 3

   lxd is not for accuracy but for stability. Typically, lxd = 3 * lx1 / 2 but can be lesser.

Hex20 = Hex8 + 12 midpoints of edges.

Therefore, when there are no curves, Hex20 = Hex8 in terms of information. 

In Nek, what we end up using is Hex (lx1^3).

Either Hex8 or Hex20 will be converted to Hex (lx1^3) using transfinite mapping (Gordon-Hall).

It's not quite the same, but when the elements are in "good shapes", lx1=3 (equivalently, Hex27) can restore the information as Hex20.

re2 is only 2nd order (unless using treatments for cylinder or sphere) and sometimes cannot capture the desired geometry.

If you really care about geometric accuracy, it's common to manually project GLL points onto the curves in usrdat2.

Hope this helps,

Yu-Hsiang

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[MWTWM M]

Dear  YuHsiang Lan

Thanks for your answer, it really helps.

 

Student Ma