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Old   September 13, 2005, 05:22
Default structured and unstructured grids
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user
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what is the difference between structured and unstructured grids? please elaborate to me. Thanks in advance.

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Old   September 13, 2005, 09:28
Default Re: structured and unstructured grids
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Myron
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Structured grids are hexahedral elements (although some of these may have co-located nodes to form degenerate elements - pyramids, prisms, etc - but still with 8 nodes). The I-J-K orientations of the blocks are preserved in the mesh structure format.

Unstructured grids may be hex-8, tet-4, prism-6, pyramid-5, etc. with the indicated number of nodes. The grid format only preserves the node number with its x-y-z location, the nearest node numbers (neighboring nodes), and which nodes are used to create the element definitions. So really just node and element definitions. Nothing about I-J-K indices in the format.
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Old   September 13, 2005, 11:45
Default Re: structured and unstructured grids
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Renato N. Elias
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Roughly speaking, In structured grids the nodes and cells are regularly placed, so you don't need any information in order to locate nodes and cells (because you will know previously where they will be).

In unstructured grids the nodes and elements may be placed in an irregular manner according to the geometry you are representing. In unstructured grids you must keep arrays with information about nodes localization (coordinates) and nodes connectivity to build the elements, but complex geometries are well represented than with structured grids.

Discrete methods such as finite differences are based on structured grids while finite elements are based on unstructured grids.

Got it?!

Regards.

Renato N. Elias

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Old   September 13, 2005, 13:35
Default Re: structured and unstructured grids
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Mani
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This question comes up once in a while and I always find that the answers are not very precise and quite easy to misunderstand. The probable reason is that there are really two different issues involved, which most people don't care to distinguish: unstructured grid (geometry), and unstructured data. Most people exclusively talk about the grids, but that's really not the divisive factor. A hexahedral grid can be treated in a structured as well as unstructured way, that's really a question of data structure. So can someone come up with a clean description? Let me try:

Structured data: Each object (e.g. cell) is identified by a unique index vector (i,j,k) which represents coordinates in a (block-)global coordinate system. Neighboring objects are identified by adding/subtracting 1 to/from either of the three indices. For example, cell (i-1,j,k) is neighbor of cell (i,j,k). The neighbors of each cell can therefore be easily identified by the topologically adjacent position vectors.

Unstructured data: Each object (e.g. cell) is identified by an arbitrary id number. Objects are ordered in an arbitrary way in a 1-D list. Consequently, additional connectivity information has to be provided to identify neighbor objects. For example, each cell definition has to include the id numbers of all connected cells.

Structured grid: A grid which is regular in the sense that it allows the application of the structured data topology. This will typically be a grid of hexahedral cells with three clearly defined coordinate directions, but could be of any other shape if cells are allowed to overlap. Although structured grids allow for structured data, they can also be used within an unstructured methodology (albeit with far less efficiency).

Unstructured grid: A grid which is irregular in the sense that it does not allow the application of the structured data topology. Unstructured data methodology has to be applied on these grids. The cell shape is arbitrary (typically polyhedrals). Grids with multiple different cell shapes are called mixed grids.

Hybrid grid: Combination of structured and unstructured grids in different (but connected) partitions of the domain.

Structured solver: Numerical algorithm which employs structured data on structured grids.

Unstructured solver: Numerical algorithm which employs unstructured data on any grid (even on structured or hybrid grids).

Hybrid solver: Solver which specifically employs a combination of structured and unstructured data on hybrid grids to exploit the efficiency of structured data, and the flexibility of unstructured data wherever possible.

Some reasons why the above distinctions are useful:

- You often hear that CFD on structured grids is more efficient that on unstructured grids of similar size. That's simply inaccurate and confusing! The efficiency is a matter of data structure, not grid geometry. An unstructured solver can apply a structured grid in a very inefficient way. It is more accurate to say that unstructured solvers (i.e. unstructured data) are more flexible and more costly than their structured counterparts.

- You often hear that structured solvers are less accurate for viscous flow than unstructured solvers. That's incorrect again. This time it really depends on grid geometry. Nicely orthogonal hexahedral cells to resolve boundary layers or shear layers can be employed by structured as well as unstructured solvers with any type of data structure.

- To clarify a common misconception: Unstructured solvers which use a combination of structured and unstructured grids are not hybrid solvers! In order to be hybrid, the solver needs to take advantage of the structured part of the grid by applying structured data (i.e. the i,j,k order) there.

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Old   September 13, 2005, 15:31
Default Re: structured and unstructured grids
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Renato N. Elias
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Mani,

According to your definitions of data/grid/solver, structured/unstructured I would do an observation:

The research group that I take part works with solvers based on edges to represent the elements in finite element computations. While working with edges is perfectly possible to get a structured representation of the unstructure grids after performing a reordering technique called "reduced reordering". This reordering is based on the work of Rainald Lohner and further details are available in the publications of this author.

Regards

Renato N. Elias

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Old   September 13, 2005, 18:27
Default Re: structured and unstructured grids
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Mani
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Yes, I was expecting somebody to comment on that. That's absolutely right and a good point. There are also many other details I neglected, just to get a simple picture.
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Old   November 25, 2010, 02:14
Default Nice explaination
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vasu
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Dear Mr.Mani
Its really a good explanation given about structured and unstructured grids.But I need to know in more detail about this even if its complex to understand.Can u please elaborate upon this?

Thanks and regards
Krishna
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