## 6.1.3 Choosing the Appropriate Grid Type

FLUENT can use grids comprised of triangular or quadrilateral cells (or a combination of the two) in 2D, and tetrahedral, hexahedral, polyhedral, pyramid, or wedge cells (or a combination of these) in 3D. The choice of which mesh type to use will depend on your application. When choosing mesh type, consider the following issues:

• Setup time

• Computational expense

• Numerical diffusion

Setup Time

Many flow problems solved in engineering practice involve complex geometries. The creation of structured or block-structured grids (consisting of quadrilateral or hexahedral elements) for such problems can be extremely time-consuming if not impossible. Therefore, setup time for complex geometries is the major motivation for using unstructured grids employing triangular or tetrahedral cells. However, if your geometry is relatively simple, there may be no saving in setup time with either approach.

If you already have a mesh created for a structured code, it will save you time to use this mesh in FLUENT rather than regenerate it. This can be a motivation for using quadrilateral or hexahedral cells in your FLUENT simulation.

Note:    FLUENT has a range of filters that allow you to import structured meshes from other codes, including FLUENT 4 (see Section  6.3).

Computational Expense

When geometries are complex or the range of length scales of the flow is large, a triangular/tetrahedral mesh can be created with far fewer cells than the equivalent mesh consisting of quadrilateral/hexahedral elements. This is because a triangular/tetrahedral mesh allows clustering of cells in selected regions of the flow domain. Structured quadrilateral/hexahedral meshes will generally force cells to be placed in regions where they are not needed. Unstructured quadrilateral/hexahedral meshes offer many of the advantages of triangular/tetrahedral meshes for moderately-complex geometries.

A characteristic of quadrilateral/hexahedral elements that might make them more economical in some situations is that they permit a much larger aspect ratio than triangular/tetrahedral cells. A large aspect ratio in a triangular/tetrahedral cell will invariably affect the skewness of the cell, which is undesirable as it may impede accuracy and convergence. Therefore, if you have a relatively simple geometry in which the flow conforms well to the shape of the geometry, such as a long thin duct, use a mesh of high-aspect-ratio quadrilateral/hexahedral cells. The mesh is likely to have far fewer cells than if you use triangular/tetrahedral cells.

Converting the entire domain of your (tetrahedral) mesh to a polyhedral mesh will result in a lower cell count than your original mesh. Although the result is a coarser mesh, convergence will generally be faster, possibly saving you some computational expense.

Numerical Diffusion

A dominant source of error in multidimensional situations is numerical diffusion (false diffusion). The term false diffusion is used because the diffusion is not a real phenomenon, yet its effect on a flow calculation is analogous to that of increasing the real diffusion coefficient.

• Numerical diffusion is most noticeable when the real diffusion is small, that is, when the situation is convection-dominated.

• All practical numerical schemes for solving fluid flow contain a finite amount of numerical diffusion. This is because numerical diffusion arises from truncation errors that are a consequence of representing the fluid flow equations in discrete form.

• The second-order discretization scheme used in FLUENT can help reduce the effects of numerical diffusion on the solution.

• The amount of numerical diffusion is inversely related to the resolution of the mesh. Therefore, one way of dealing with numerical diffusion is to refine the mesh.

• Numerical diffusion is minimized when the flow is aligned with the mesh.

This is the most relevant to the choice of the grid. If you use a triangular/tetrahedral mesh, the flow can never be aligned with the grid. If you use a quadrilateral/hexahedral mesh, this situation might occur, but not for complex flows. It is only in a simple flow, such as the flow through a long duct, in which you can rely on a quadrilateral/hexahedral mesh to minimize numerical diffusion. In such situations. It is advantageous to use a quadrilateral/hexahedral mesh, since you will be able to get a better solution with fewer cells than if you were using a triangular/tetrahedral mesh.

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