What is the usual role of pyramid cells?

Transition between hexahedral and tetrahedral regions

Extruding from surface meshes for inflation layers

Why are thin stretched prism (inflation) layers used at walls?

Gradients are steepest normal to the wall, so many cells are needed only in that direction

To make the mesh isotropic near the wall

To make the first cell as thick as the boundary layer

Which describes a good prism layer set-up?

Small first-layer height set from the required y+, growth ratio about 1.1 to 1.3, total thickness about the boundary layer thickness

Constant layer height equal to the core cell size

Growth ratio of 3 to reach the core quickly

First-layer height chosen irrespective of the turbulence model

Practice · 5 marks

2D and 3D mesh elements, prism layers

Short answer

Common 2D elements are triangles (easy automatic meshing) and quadrilaterals (higher accuracy when aligned). 3D elements include tetrahedra, hexahedra, prisms, pyramids, and polyhedra. Prism (inflation) layers are thin stacked prismatic cells near walls, with a growth ratio, used to resolve steep normal gradients, meet y+ requirements, and reduce numerical diffusion for accurate wall shear and heat flux.

Describe the common 2D and 3D mesh element types used in CFD. What are prism (inflation) layers and why are they used?

2D elements

Triangle: three nodes; fits any boundary, fully automatic generation, but needs more cells and gives more numerical diffusion if not aligned with flow.
Quadrilateral: four nodes; good accuracy when aligned with the flow, fewer cells, preferred in boundary layers and simple shapes.

3D elements

Element	Faces	Features
Tetrahedron	4 triangles	Easy automatic meshing of any CAD; large cell count; poor in thin boundary layers
Hexahedron	6 quads	Highest accuracy and lowest cell count; hard to generate for complex shapes
Prism (wedge)	2 triangles + 3 quads	Used for boundary layers; extruded from a surface triangle mesh
Pyramid	1 quad + 4 triangles	Transition between hexa and tetra regions
Polyhedron	Any number of faces	Created by merging tetra cells (e.g. in Fluent); fewer cells, more neighbours, good gradients

 tetra     hexa        prism       pyramid
   /\      +----+      /|--|\       /\
  /__\     |    |     / |  | \     /  \
  \  /     +----+     \_|__|_/     +---+

Prism (inflation) layers

Prism layers are several thin layers of prismatic (or hexahedral) cells stacked from a wall, with the first-layer height small and each layer thicker than the previous by a growth ratio (usually 1.1 to 1.3).

Reasons for use:

Velocity and temperature gradients are steepest normal to the wall, so many cells are needed in that direction only; stretched cells save cell count.
The first cell height can be set to meet the required $y^+$ for the turbulence model (about 1 for wall-resolved, 30 to 300 for wall functions).
Cells aligned with the wall reduce numerical diffusion and improve wall shear stress and heat flux prediction.
Total layer thickness should be about the boundary layer thickness, with smooth transition to the core cells.

✓ Answer checked by Claude Opus 5.5 (high effort)

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2D and 3D mesh elements, prism layers

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