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Anurag Sharma September 22, 2005 00:39

Hello everyone
Hello everyone,

It gives me great pleasure to introduce myself to you all. Jonas has been kind enough to accept me into the Wiki editors team.

I have around 10 years of experience in various aspects of mesh generation, but mostly in the field of unstructured mesh generation. Currently I am involved in automated adapted Cartesian mesh generation technology.

I look forward to interact with you all and contribute to this Wiki.

Regards Anurag

zxaar September 22, 2005 01:02

Re: Hello everyone
what is adapted Cartesian mesh , i had something in my mind, i wonder it is the same thing.

Anurag Sharma September 22, 2005 01:10

Re: Hello everyone
You can find out more details from this paper:

Praveen. C September 22, 2005 23:10

Re: Hello everyone
I have not seen any applications of Cartesian grids for turbulent Navier-Stokes computations. Is it possible with Cartesian grids ? Can you give some references ?

Anurag Sharma September 23, 2005 01:19

Re: Hello everyone
Hi Praveen.

Let me clarify a bit. I may have used the term Cartesian meshes a bit loosely.

Cartesian meshes, by definition, are structured meshes whose grid lines are all aligned with Cartesian axes. For such meshes, it is sufficient to store the node indices in X, Y and Z directions to completely define the mesh node locations and cell connectivity.

However, adapted Cartesian meshes introduce hanging nodes on edges and faces to allow change in cell size from one location of the mesh to another. Obviously, more information needs to be stored to still clearly define connectivity.

Furthermore, it is possible to refine the mesh according to domain surface curvature. Also, as a final step, mesh cells outside the domain can be deleted and the boundary of the resulting mesh can be modified to match the domain. Resulting meshes still are predominantly Cartesian, though boundary cells are not. Finally, meshes can be smoothed. However, once meshes are smoothed or modified to match the domain, they lose their Cartesian nature.

You can see the snapshots of such meshes on Michal Aftosmis' page (follow the link to Cart3d). You can also check the link to HEXPRESS ( and Harpoon ( meshers.

What is important to note is that most advanced solvers read meshes in unstructured format. Therefore, even if the mesh is originally created as Cartesian, it is exported as unstructured (which does not store the Cartesian nature of the mesh). Many NS solvers having turbulence capabilities can read in adapted meshes.

Why use Cartesian meshing when resulting meshes anyway get exported as unstructured? For speed and memory considerations. Cartesian evaluations are much faster, and it is possible to store Cartesian cells with much smaller memory usage.

Voxel based solvers like Exa ( solve on Cartesian meshes. However, Exa is based on statistical models like Boltzman-Lattice, if I am not wrong.

Hope this helped. Anurag

Praveen. C September 23, 2005 02:16

Re: Hello everyone
Thanks for the explanation. I am familiar with the type of meshes you are talking about. The reason I asked the question is because I have seen some papers where turbulent NS results on Cartesian grids are not good.

How would one generate the highly stretched cells necessary in a turbulent boundary layer with the Cartesian method ? This is very important to resolve the boundary layer and the first point above the wall needs to be at a distance of the order of 1e-6 sometimes.

Jonas Larsson September 23, 2005 04:31

Re: Hello everyone
People are working hard on creating cartesian meshers that also can create resolved boundary layers with boundary-fitted cells (hex or prism layers). Take a look at for example harpoon from cei:

This is a really hot subject in commercial CFD. Most big CFD companies have projects on cartesian meshers. The trend was started by Marsha Berger (Courant Institue) and John Aftosmis (NASA Ames). See:

They've done some really impressive work on aircraft external aerodynamics.

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