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Andrew Epp December 8, 1998 14:07

Mesh Compatibility

I was hoping that someone could tell me which of the following grids are incompatible and why?

rectilinear uniform, triangular structured, multi-block unstructured, curvilinear orthogonal

thank you very much, Andrew Epp

andy December 8, 1998 14:16

Re: Mesh Compatibility
Incompatability is likely lie with the solvers and not the grids. Some solvers can work with only rectilinear grids whereas others can work with all the ones you have listed.

sampige December 8, 1998 17:21

Re: Mesh Compatibility
I'm not quite sure what you mean by "incompatible grids," but I'll take a shot at answering you Q. To be sure Andy's answer is appropriate. The "correctness" of the grid really depends on if your solver can handle it. However, here goes my answer...:

There no such thing as a "structured triangulation" but 2D structured meshes can be combined w/ triangulations ( to give "hybrid" grids)

Ditto for "multi-block unstructured." My understanding is that that is a loose usage. "multiblock" is generally a term used w/ structured grids, even though recently i did hear "multi-block unstructured" which in my opinion is poor usage since the "block" and "unstructured" don't go together.

Ditto again for "curvilinear orthogonal." This one is a little more ambiguous to label as poor usage. You have curvilinear coordinate systems within which you can have some orthogonal cells in physical space but cannot enforce this orthogonality everywhere in every case (in computational space, they're all orthogonal anyways...) But I've never heard the usage of "curvilinear orthogonal" grids.

I've not even ever heard of "rectilinear uniform." I've heard "uniform cartesian" But "uniform rectilinear" is new to me (maybe I'm new to it...getting too old perhaps...)

Were these the answers you were looking for when you asked about "incompatible grids" ?

jay December 8, 1998 17:52

Re: Mesh Compatibility
I think "curvilinear orthogonal" or "orthogonal curvilinear" is pretty standard terminology.

John C. Chien December 8, 1998 18:47

Re: Mesh Compatibility
Most likely, you are going to see " unstructured triangular mesh " and " structured multi-block mesh ". Since it is hard to use structured mesh ( labeled i=1 to in, j=1 to jn, and k=1 to kn ) to cover complex geometry, people normally use multi-block approach to cover the flow field so that each block can have their own labeling system and have common interfaces. So the multi-block approach was invented originally for the structured mesh ( H-type mesh, C-type mesh, O-type mesh etc.). To break this limitation, people try to fill the flow field with different sizes element without particular order, as long as the flow field is covered with these elements. ( the idea comes originally from finite element people doing structure analysis, now call finite-element analysis). These elements in 2-D can be either three-sided or four sided. This is normally called " unstructured triangular mesh" for three-sided elements. This is how it's normally used because it has great impact on the subsequent derivation of numerical formulation in order to solve the set of governing equations.

P.Jawahar December 10, 1998 01:50

I think, "structured triangular" mesh is used to indicate "triangulated" "structured" mesh. Here the word "structured" is used loosely to indicate that the unstructured mesh was generated using the points obtained from the structured grid.

Consider generating a grid around NACA 0012 airfoil with circle as the outer boundary. You can generate both structured (quadrilateral elements) and unstructured (triangular elements) grids for this configuration quite easily.

Suppose you have an unstructured grid generator, say, based on Delaunay triangulation technique. You have to introduce interior points once the boundary triangulation is over. There are several ways of introducing these 'interior points' in a typical unstructured grid generation. However, one has the option of introducing the points obtained from a structured grid also. The resulting grid exactly looks like that of the structured grid but with the diagonals of the quadrilateral joined giving a triangular(almost right-angle triangles) mesh. I understand that this is widely referred to as "structured triangulated" mesh.

This has got the following "constraints" of structred mesh: * One-to-one correspondence between the boundary points which forces one to take same number of points both on the solid wall and the outer boundary(where one doesn't need that many). * difficult to extend to complex geometries!

But it has the advantage of ensuring smooth distribution (clustering) of cells which enables one to get a good quality viscous solution in an unstructured mesh frame work. Note that "most" of the "unstructured viscous computations" use such grids ! In short, one has the control over this "structured triangulated" grid which can be used in an unstructured environment ! I guess grid control is one of the key issues in unstructured grid generation :)


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