Volume Meshing

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.

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

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

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

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

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

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

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)

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

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

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

Troubleshooting the Cooper Tool A 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.

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

Troubleshooting the Cooper Tool A 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.

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

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

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

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

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

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.

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

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.

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

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

Appendix

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.

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

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

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