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Old   December 11, 2006, 03:49
Default Hyperbolic mesh generator
  #1
Martin
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Hi,

I am writing hyperbolic mesh generator for structured meshes around airfoils in 2D and I have following question:

is there some good cell volume specification especially for concave regions? Specification I use causes too slow mesh extrusion from concave regions even with low depth or creates "bubbles" in this places. Is it generally possible to create hyperbolic meshes around concave regions (e.g. around space between main wing and flap). An example of such hyperbolic mesh can be seen at http://www.pointwise.com/images/mfoila.gif http://www.pointwise.com/images/mfoilb.gif http://www.pointwise.com/images/mfoilc.gif http://www.pointwise.com/images/mfoild.gif

Does anybody know how to create such mesh? Is it generally possible to create such meshes or this one is only carefully selected exceptional case?

Thanks
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Old   December 11, 2006, 07:03
Default Re: Hyperbolic mesh generator
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Harish
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Depending on your necessity there are different algoritms available for generation of hyperbolic meshes.For the case of an airfoil there is a paper

Orthogonal grid generation for Navier-Stokes computations Manoj T. Nair, T. K. Sengupta International Journal for Numerical Methods in Fluids Volume 28, Issue 2 , Pages 215 - 22

where they solve the incompressible N-S equation in covariant form.There are some papers which extend the hyperbolic grid generation method even to internal flows.

You might need to add a laplacian dissipation operator to the hyperbolic grid generator for smoothing.

Regarding the pictures you showed it is possible to generate such meshes using hyperbolic grid generation.But its not at the click of a button.

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Old   December 16, 2006, 15:36
Default Re: Hyperbolic mesh generator
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John Chawner
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Martin,

The hyperbolic PDE method can generate meshes off concave regions. The examples you cite from Pointwise's web site are not exceptional cases and do not require significant effort to setup. (That doesn't mean that it didn't require a lot of work to program.)

Having written that, the hyperbolic method is extremely fragile. After all, a hyperbolic system tends to propagate discontinuities in the marching direction. So any slope changes or geometric breaks on the intial front (the grid on the surface) tend to propagate onto the interior of the grid.

That's why hyperbolic grid generators tend to have so many user-definable smoothing controls. The basic method (from the work of Steger) includes both implicit and explicit smoothing coefficients. An invaluable addition to the hyperbolic method is something we call the Kinsey-Barth factor (after the authors of the paper describing the technique).

Does your implementation have something called volume averaging? This technique tends to drive the cells to equal sizes as the grid is marched away from the body. By doing so, any unequal grid spacings along the original grid are smoothed.

From a practical standpoint, any slope discontinuity on the intial grid (like a sharp corner) needs to have grid points spaced equally on either side. For example, you don't want the cell on the left side of a corner to be 5 times the size of the cell on the right.

Chan from NASA Ames Research Center has published a large number of papers on hyperbolic grid generation methods and many of those publications are AIAA papers. Chan also publishes a lot at the bi-annual Overset Symposium. You might want to add his work to your literature search.

Hope this helps.
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Old   December 26, 2013, 15:22
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Quote:
Originally Posted by Martin
;46955
Hi,

I am writing hyperbolic mesh generator for structured meshes around airfoils in 2D and I have following question:

is there some good cell volume specification especially for concave regions? Specification I use causes too slow mesh extrusion from concave regions even with low depth or creates "bubbles" in this places. Is it generally possible to create hyperbolic meshes around concave regions (e.g. around space between main wing and flap). An example of such hyperbolic mesh can be seen at http://www.pointwise.com/images/mfoila.gif http://www.pointwise.com/images/mfoilb.gif http://www.pointwise.com/images/mfoilc.gif http://www.pointwise.com/images/mfoild.gif

Does anybody know how to create such mesh? Is it generally possible to create such meshes or this one is only carefully selected exceptional case?

Thanks

Your attached pictures for the airfoil mesh looks amazing to me. Are them generated automatically? Where software can do that?
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Old   December 29, 2013, 17:09
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Anna:

The images you asked about come from our website and were generated using Pointwise's hyperbolic mesh generation technique.
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Old   January 1, 2014, 04:42
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