# What does mesh topology mean?

What is a mesh topology? I have read this term being used in a lot of articles dealing with meshing the computational domain, but could not understand its intuitive meaning. And why is topology called a global property? Also, what does topology mean wrt CFD analysis anyways? Thank you.

Depending on the context, mesh topology is the cell or mesh density and how it changes across the whole calculation field.

To get detail then the computational area is divided into cells - more cells means better detail / results but at a cost of more calculations ie it takes longer.

So, engineers look to “target” extra cells in areas of importance or relevance by increasing the mesh density in those areas and leaving other areas with fewer cells to limit or reduce the total number of cells so controlling the total time to calculate .

Some jobs I did ran for 40 days ie 40 * 24 hours - any reduction due to optimisation of the calculation field was welcome and looked for...

• What does it mean to say that the topology of the mesh remains invariant under mesh smoothing? Jun 27 '18 at 8:07
• What does “invariant” mean? What is “mesh smoothing”? Jun 27 '18 at 8:10
• Invariant means "does not change with" or nor a function of I would guess. I think of Mesh smoothing as a process usually after we have generated a mesh to improve quality of mesh by moving or "wiggling around" the different node points. Jun 27 '18 at 8:20
• Now think about “wuality of mesh” and my answer ... define quality.... Jun 27 '18 at 8:23
• "Quality" I would say, if need to be quantified, as a function of various element properties like its skewness, aspect ratio, orthogonality etc. Jun 27 '18 at 8:31

Quoting from one paper related to FEA,

The output of a mesh generator consists of a set of nodes, and a set of elements (which represents the mesh topology). [...] The nodes are created first, and they are then connected to form triangular or quadrilateral elements. This can be divided into two subcases. If the vertexes of the object are assumed to be the only nodes in the mesh, a triangulation algorithm can be applied to create a minimum number of nonoverlapping triangles that cover the object (see Figure 10). This minimal set of triangles is determined mainly by the topology of the object. The complex topology of the object has been decomposed into the simple topology of the triangles, so this approach will be called the topology decomposition approach. The mesh thus created has distorted and mostly coarse elements, and cannot be used for analysis purposes. Mesh refinement, possibly with element rearrangements by the diagonal transpose technique, must be applied to produce a reasonable mesh.

So, colloquially, "mesh topology" may be used to indicate node density variations, face orientation variations, etc. (The term "topology" itself comes straight from mathematics, where it means the study of sets and surfaces. )

• In this paper what does topology of the object mean?. Jun 27 '18 at 20:24
• What do you think it means? @GRANZER Jun 27 '18 at 21:40
• @SolarMike I would assume they are talking about the CAD object and not the actual real object. How this CAD object is made of vertices, lines, and surfaces. Jun 28 '18 at 9:07

Mesh topology, just like the mathematical definition of a topology, defines how things are connected or related. The meshing of a computational domain is made up of nodes and elements(take here line elements ie line connecting one node to another). Topology means how these nodes are connected by elements as the same nodes could be connected in other ways too and this would be another topology. If the mesh is considered as a set, and the nodes and elements are considered the part of this set then topology is how all these parts are connected or related to each other. There are different topologies on the same set.

• you may need to add a picture Jun 29 '18 at 5:08
• @joojaa What picture you had in mind? Jun 29 '18 at 9:48
• one that shows 2 different mesh topologies for same boundaries. It shouldnt take any of you more than 2 minutes to make. I mean i would do it but i have no computer at the moment. Jun 29 '18 at 11:10