1. Volume Meshing

2. Approach
A high-quality hex mesh is generally preferred over a tet mesh.
Reduced discretization error and false numerical diffusion for a given mesh size.
Significantly lower cell count
Example:
Compare the cell count for a 10×10×10 cube using hex and tet with a cell size of 1.
Hex mesh generates 1,000 cells.
Tet mesh generates 7,726 cells!
For a hex mesh, geometries typically need to be decomposed into simpler ones so that one of the hex meshing schemes can be used.
In some cases, the geometry can be very complex.
Hex meshing can be expensive or impractical.
In these cases, a tet or hybrid mesh is preferred in order to reduce meshing effort.

3. Volume Meshing Upon picking a volume
GAMBIT will automatically choose a type based on the solver selected and the combination of the face Types of the volume.
In ambiguous cases, GAMBIT chooses the Tet/Hybrid: TGrid combination
Available element/scheme type combinations
Hex
Map, Submap, Tet Primitive, Cooper, Stairstep
Hex/Wedge
Cooper
Tet/Hybrid
TGrid, HexCore

4. Volume Meshes - Hex Examples
Hex – Map
Hex -- Submap
Hex – Tet Primitive
Hex – Cooper

5. Hex/Wedge and Tet/Hybrid Examples
Hex/Wedge: Cooper
Tet/Hybrid: TGrid
Tet/Hybrid: HexCore

6. Hex Meshing – Map A mappable volume: Is a logical cube
Has all faces either mappable or submappable
Has topologically matching mesh on all faces.
Mesh
submap face
Mesh

7. Hex Meshing – Submap A submappable volume:
Has all faces either mappable or submappable.
Has topologically matching opposite faces.
Mesh
Mesh

8. Hex Meshing – Tet Primitive
Tet-Primitive scheme
All hex elements in a four-sided (tetrahedral) volume
Volumes directly meshable using Tet Primitive scheme
How the tet primitive scheme works
Connect center points on edges, faces and the volume
Mesh the four subvolumes using the map scheme.
Mesh

9. Hex Meshing – Cooper
The Cooper scheme projects or extrudes a face mesh (or a set of face meshes) from one end of a volume to the other and then divides up the extruded mesh to form the volume mesh.
The projection direction is referred to as the Cooper direction.
Faces topologically perpendicular to this direction are called source faces.
Source faces need not be premeshed.
At least one source face must not be meshed and must span the entire cross section.
Faces that intersect the source faces are referred to as side faces.
Side faces must be either mappable or submappable
Cooper
direction
Source Faces
Side Faces (two hidden)

10. Cooper Examples Volume Containing Multiple Holes
source faces
source faces
source faces
Volume Containing Multiple Holes
Multiple Source Faces and Multiple Interior Loops
Source Faces Not Parallel

11. Cooper Tool Methodology
When the Cooper scheme is selected, a source face list box appears in the panel.
If GAMBIT chooses the sources faces
Check the source face list and verify that GAMBIT has chosen the correct faces.
If necessary, change the source faces selection.
GAMBIT may not be able to resolve the source faces
Manually select the source faces
If necessary, manually change the vertex types (discussed in lecture 3) on some of the side faces

12. Troubleshooting the Cooper ToolA B C
Problem:
Source faces A, B, and C are premeshed. The Cooper tool fails. Why? How can this volume be meshed?

13. Troubleshooting the Cooper ToolA B C
Solution:
The mesh on source faces A and B cannot be projected onto face C (the source faces are overconstrained. Delete the mesh on face C in order to generate the volume mesh.

14. Troubleshooting the Cooper ToolA B C
Problem:
A brick is split as shown. The Cooper tool fails. Why? What can be done to generate a volume mesh?

15. Troubleshooting the Cooper ToolA B C A1
Volume 1
Volume 2 C1
Solution:
Cooper tool fails because no logical axis exists. If faces A and B are source faces, then face C must be either mappable or submapple. Face C contains a void and can only be paved. Split the volume with a face as shown. Use Face A1 as one source face for volume 1 and use face C2 as one source face for Volume 2.

16. Troubleshooting the Cooper ToolA B
Interior loops
Problem:
The Cooper tool fails because the interior loops on source faces A and B either overlap or are close.

17. Troubleshooting the Cooper ToolA A1 A2
Interior loops B
Solution:
Split source face A as shown. Neither face A1 nor A2 contain closed interior loops.

18. How to Make a Volume Cooperable
Three options to use the Cooper Tool:
Manually change vertex types on the side faces to make them mappable or submappable.
Manually select the source faces. GAMBIT will attempt to make side faces mappable or submappable.
Enforce the map or submap scheme on the side faces.
Example: manually change the vertex types
3 Source Faces S E S E C C E E E E E E

19. Tet/Hybrid Meshing Tetrahedral/Hybrid Mesh Scheme - TGrid
Most volumes can be meshed without decomposition, regardless of complexity.
Use boundary layers to create hybrid grids (prism layers on boundaries to capture important viscous effects).
Use on volumes that are adjacent to volumes that have been meshed with hex elements will automatically result in a transition layer of pyramids. 1
Hex Cooper 2
Tet: TGrid
Pyramid
layer 3
Hex/Wedge
Cooper

20. Tet/Hybrid Meshing – Troubleshooting
Quality of the tetrahedral mesh is highly dependent on the quality of the triangular mesh on the boundaries.
Initialization process may fail or highly skewed tetrahedral cells may result if there exists:
highly skewed triangles on the boundaries.
large cell size variation between adjacent boundary triangles.
small gaps that are not properly resolved with appropriately sized triangular mesh.
Difficulties may arise in generating hybrid mesh.
Cannot grow pyramids from high aspect-ratio faces.
Prism and pyramid generation may not work properly between surfaces forming very small angles.
Prism layer
small angle
Low-quality pyramid

21. HexCore Meshing
Combines Tet/Hybrid mesh with Cartesian mesh in the core.
Fewer cells with full automation and geometric flexibility.
Important HexCore defaults:
Hexcore_Offset_Layers
The number of offset layers (cell layers between wall and hexahedral core); default value is 3.
Hexcore_Quad_Surface_Split
Controls quad/tri splitting and eliminates pyramid cells when turned on; see Appendix
Hexcore_Method
Controls the method used to create HexCore – Standard or TGrid HexCore.
TGrid HexCore requires specification of buffer layers.

22. Flow Volume Around a Boat Hull
HexCore Meshing
Flow Volume Around a Boat Hull
Flow Volume Inside an
Automobile Manifold

23. Assigning Boundary and Continuum Types
Boundary Type Form
Enter entities to be grouped into single zone in entity list box.
First choose entity type as face or edge.
Select boundary type for zone (entity group).
Available types depend on Solver
Name zone if desired.
Apply defines zone and boundary type.
Can also modify and delete zone/boundary.
By default,
External faces/edges are walls
Internal faces/edges are interior
Continuum Type form
Continuum types are defined in a similar way as boundary types.
Multiple fluid/solid zones can be defined.
Unspecified continuum zones are always assigned the fluid type.

24. Example: Flow over a Heated Obstacle
Boundary
Name = inlet
Type = VELOCITY_INLET
Boundary
Name = outlet
Type = PRESSURE_OUTLET
Continuum
Name = obstacle
Type = SOLID

25. Defaults: Example: Flow over a Heated Obstacle
By default, the 4 remaining external faces have the Name and Type:
Boundary: Name = wall
Type = WALL
By default, the one remaining volume has the Name and Type
Continuum: Name = fluid
Type = FLUID

26. Appendix

27. Meshed Size Function from Boundary Layer Cap
Meshed Size Function starting from boundary layer cap improves size transition between the boundary layer and volume mesh.
Useful for external aerodynamics applications.
Specify the Growth Rate and Max. Size for the mesh growing from the last prism layer into the volume.
Example: 3D wing profile with 12 boundary layers; the meshed size function is used for smooth transition to the tet volume mesh.

28. Hex-Core Meshing – Surface Split Options
Geometry: Cylinder
Edit Default: Mesh.Cartesian.Hexcore_Quad_Surface_Split
1 (default)
Split boundary quad into 2 triangles
hanging edges created (NOT allowed in FIDAP)
Smooth boundary hexes with larger hexcore
Boundary quads are NOT split
Pyramid (transition) elements created
Boundary hexes not smoothed

29. FIDAP 8 Example: Flow over a Heated Obstacle
Boundary: Name = outlet
Type = PLOT
Continuum: Name = step
Type = SOLID
Boundary: Name = outlet
Type = PLOT

30. Linear/Quadratic Elements (FIDAP/POLYFLOW USERS ONLY)
General tools
Higher-order elements
For FEM codes (FIDAP and POLYFLOW), the element order can be changed at all three meshing levels
Only linear and quadratic elements are directly available
A change to quadratic element type at one level will automatically change the element type in other levels
The following table presents the most commonly used and recommended quadratic element types for FEM solvers
POLYFLOW FIDAP
Edge 3-node 3-node
Face 8-node quad 9-node quad
Volume 21-node brick 27-node brick