gambit-VolumeMesh

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Introductory GAMBIT Notes GAMBIT v2.0 Jan 2002

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Volume Meshingand the

Sizing Function

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Approach

u To potentially reduce discretization errors, and to reduce cellcount, a ‘high’ quality hex mesh is preferred.l For a hex mesh, complicated geometries (volumes) typically need to

be decomposed into simpler ones so that one of the hex meshingschemes can be used.

l In some instances, some geometries may be too complex anddecomposition for hex meshing is impractical or impossible. In theseinstances use a tet/hybrid mesh.

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Volume Meshingu Volume Meshing Form:

l Upon picking a Volumen GAMBIT will automatically choose a Type based on the solver selected and

the combination of the face Types of the volume.n In ambiguous cases, GAMBIT chooses the Tet/Hybrid: TGrid combination

l Available element/scheme type combinationsn Hex

s Maps Submaps Tet-Primitives Coopers Stairstep

n Hex/Wedges Cooper

n Tet/Hybrids TGrid

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Volume Meshes - Hex Examplesu Hex: Map

u Hex: Submap

u Hex: Tet-Primitive

u Hex: Cooper

u Hex: Stairstep

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Hex/Wedge and Tet/Hybrid Examples

u Hex/Wedge: Cooper

u Tet/Hybrid: TGrid

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Hex Meshing - Map

l Volumes that are mappable by default: n A logical cube n All faces map-able (or Submap-able) and mesh is matching

u Map Scheme

mesh

mesh

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Hex Meshing - Submap

l Volumes that are Submap-able by default:n All faces map-able or submap-ablen Topological matching of opposite faces

u Submap Scheme

mesh

mesh

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Hex Meshing - Tet-Primitive

l All hex elements in a four-sided (tet) volumel Volumes directly meshable using Tet-Primitive scheme

l How the Tet Primitive Scheme worksn Connect center points on edges, faces and the volumen Map the four sub-volumes

u Tet-Primitive scheme

Tet Primitive

Mesh

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Hex Meshing - Cooperu The Cooper Scheme, in essence, projects or extrudes a face mesh (or a set

of face meshes) from one end of a volume to the other and then divides upthe extruded mesh to form the volume mesh.l The projection direction is referred to as the Cooper direction.l Faces topologically perpendicular to this direction are called Source faces.

n Source faces do not have to be premeshed.n In practice, at least one source face must not be meshed and must span across

the entire cross section.l Faces that intersect the source faces are referred to as Side faces.

n Side faces must be Mappable or Submappable.

Cooper direction

Source Faces Side Faces

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Permissible Cooper Geometriesu Cooper Scheme - permissible geometries

l A volume with multiple source faces on multiple sidesl Holes or “wells” are allowed

source faces

source faces

source faces

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Impermissible Cooper Geometries

u Cooper Scheme -impermissible geometriesl (a) Cannot construct logical

cylinder, the side faces ofwhich is mappable

l (b) All source faces aremeshed

l (c) Cannot use Cooper(readily) with multiple sourcefaces on opposing ends.

(c)

(a)

(b)

A

B

C

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Cooper Applicationu Cooper scheme - Application

l When the Cooper scheme is selected, asource face list box appears in the panel.

l GAMBIT will automatically select allsource faces for direct Cooper-ablevolumes (scheme comes up as default).

l If GAMBIT chooses the sources faces, you should check the source face list andvisually check for an intelligent selection. Change, if necessary.

l If GAMBIT fails to pick a set of source faces, you can either manually changethe vertex types on the side faces or manually select the source faces.

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Hex Meshing - Stairstep

u The Stairstep scheme creates a single-block structured mesh.u The Stairstep scheme creates and meshes a faceted volume the shape of

which approximates the volume to be meshed.l The original volume is not meshed.l Faceted volume:

n is generated as a result of the meshing processn is not connected to original volume.

l Assignment of continuum and boundary zonetypes must be applied to faceted volume.

u The Stairstep scheme can be used for quickmesh when boundary mesh is less important.l ‘Body-fitted’ boundary mesh will

be implemented in future.

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Tetrahedral/Hybrid Meshingu Tetrahedral/Hybrid Mesh Scheme - TGrid

l Automatic - most volumes can be meshed without decomposition.l Use boundary layers to create hybrid grids (prism layers on boundaries to

capture important viscous effects).l Using on volumes that are adjacent to volumes that have been meshed

with hex elements will automatically result in a transitional layer ofpyramids.

Hex mesh first

Tet mesh second

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Tet/Hybrid Meshing: Troubleshooting

u Quality of the tetrahedral mesh is highly dependent on the quality ofthe triangular mesh on the boundaries.l Initialization process may fail or highly skewed tetrahedral cells may

result if there exists:n highly skewed triangles on the boundaries.n large cell size variation between adjacent boundary triangles.n small gaps that are not properly resolved with appropriate sized

triangular mesh.

u Difficulties may arise in generation of hybrid mesh.l Cannot grow pyramids from high aspect-ratio faces.l Prism and pyramid generation may not work properly between surfaces

forming very acute angles.

low quality pyramid

prism layer

acute angle

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Sizing Functionsu Sizing Function controls mesh distribution in a region of space

(Edges, Faces, and Volumes) in a manner analogous to the waygrading controls mesh distribution on edges.

u Sizing Function accessed through Toolbar:

Without a Size Function With a Size Function

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Sizing Function Types

u Sizing Function requires the specificationof Type, Entities, and Parameters.

u Sizing Function ‘Type’ controls methodby which scope of sizing function isobeyed.l Fixed

n Scope is defined as a fixed region abouta source.

l Curvaturen Scope is defined as a region near highly

curved surfaces.l Proximity

n Scope is defined as a region within aspecified distance from objects.

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Sizing Function Definitionu Each Sizing Function Type requires the

specification of:l Entities

n Source entity defines shape and location of the‘origin’ of affected region.

n Attachment entities host the mesh that will beaffected.

l Parametersn Defines growth rate of cells in affected region for

Fixed and Curvature Type.n Defines number of cells in gaps for Proximity

Type.n Defines extent of affected region in Attachment

entities.n Defines maximum cell size allowed in affected

region.

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Fixed Sizing Function - Sourceu Source

l Can be vertices, edges, faces, or volumesl Can be internal or external to attachment entitiesl Source entity defines shape of scope

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Sizing Function - Attachments

u The attached entities host mesh to be affected.

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Fixed Sizing Function - Parameters

u Start sizel Size adjacent to the source

u Growth ratel Ratio of two adjacent mesh-element

edge size

u Distancel Determine boundary of size function

u Size limitl Maximum allowable size for

attachment entity

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Curvature Sizing Functionu Modifies size according to geometric

curvatureu Sources can only be face entitiesu Parameters

l Angle - Maximum allowable angle betweenoutward pointing normals for any twoadjacent mesh elements located immediatelyadjacent to the surface of a source

l Others are as with Fixed

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Proximity Size Functionu Specifies number of cells in face gap (3D) and

edge gap (2D)u Parameters

l Cells per gap - number of mesh layers in the gap.l Distance - maximum distance from the source at

which size function applies.l Size limit

u Limitationsl Becomes slow on large modelsl Improper use may result in abrupt change in sizel Solutions

n Use multiple size functionsn Specify large value for distancen Increase resolution by changing the defaults for

background grids

Documents

gambit-VolumeMesh