Hyperbolic mesh generator
 

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

Re: Hyperbolic mesh generator
 

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.

Re: Hyperbolic mesh generator
 

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.

Your attached pictures for the airfoil mesh looks amazing to me. Are them generated automatically? Where software can do that?

Anna:

The images you asked about come from our website and were generated using Pointwise's hyperbolic mesh generation technique.

Hi Harish. I too am generating a hyperbolic grid using C programming around an airfoil using arc length control. I have generated the airfoil but couldnot generate the grid properly. Could you please guide me towards sources which would help me in the same.
Thanks

hi
i dont know how to mesh 3 airfoils like this , could U pls give this file to me that i see how you block it ?

Hello Sina:

Create connector(s) around the perimeter of each component of the airfoil. Connect the trailing edge of the slat to the leading edge of the main element and the trailing edge of the main element to the leading edge of the flap using connectors. The initial extrusion front (in 2D) will be a loop of connectors from leading edge of the slat around the entire collection and ending back at the slat leading edge. (Or you could do it from flap trailing edge. Doesn't matter.) Then create a domain by extruding from that front using the Normal/Hyperbolic technique.

Good Luck