Types of mesh

In computational solutions of partial differential equations, meshing is a discrete representation of the geometry that is involved in the problem. Essentially, it partitions space into elements (or cells or zones) over which the equations can be approximated. Zone boundaries can be free to create computationally best shaped zones, or they can be fixed to represent internal or external boundaries within a model.

In addition, meshes also find extensive use in the analysis of geographical and cartographic data.

The mesh quality can be conclusively determined based on the following factors.

The greater the rate of convergence, the better the mesh quality. It means that the correct solution has been achieved faster. An inferior mesh quality may leave out certain important phenomena such as the boundary layer that occurs in fluid flow. In this case the solution may not converge or the rate of convergence will be impaired.

A better mesh quality provides a more precise solution. For example, one can refine the mesh at certain areas of the geometry where the gradients are high, thus increasing the fidelity of solutions in the region. Also, this means that if a mesh is not sufficiently refined then the precision of the solution is more limited. Thus, mesh quality is dictated by the required precision.

CPU time is a necessary yet undesirable factor. For a highly refined mesh, where the number of cells per unit area is maximum, the CPU time required will be relatively large. Time will generally be proportional to the number of elements.

Once the computations are done and the desired property of fluid does not vary with respect to different mesh elements then it represents that further change in elements doesn't vary your results and is termed as Independent Grid. This is an essential tool to know how good you mesh from the point of purpose of comparative results.

There are two types of two-dimensional cell shapes that are commonly used. These are the triangle and the quadrilateral.

Computationally poor elements will have sharp internal angles or short edges or both.

This cell shape consists of 3 sides and is one of the simplest types of mesh. A triangular surface mesh is always quick and easy to create. It is most common in unstructured grids.

This cell shape is a basic 4 sided one as shown in the figure. It is most common in structured grids.

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