Difference between revisions of "OpenFOAM/C3/Introduction-to-SnappyHexMesh/English"

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(Created page with 'Tutorial: Introduction to snappyHexMesh in OpenFOAM. Script and Narration: Chaitrali Ghodke. Keywords: Import STL file, background hex mesh, snappyHexMeshDict. {| style="…')
 
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|-
 
|-
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| Slide 2 : Learning Objectives
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| Slide 2 : Learning Objectives
 
 
  
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| In this tutorial, we will learn about  
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| In this tutorial, we will learn about  
  
* The parameters in '''snappyHexMesh''' to generate '''Mesh''' in '''OpenFOAM'''.
+
* The different parameters in '''snappyHexMesh''' to generate '''Mesh''' in '''OpenFOAM'''.
 
+
 
+
  
 
|-
 
|-
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| Slide 2: Pre-requisite
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| Slide 2: Pre-requisite
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| As a pre-requisite, the user requires
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| As a pre-requisite, the user requires
 
  
 
* Surface data files in '''STL''' format
 
* Surface data files in '''STL''' format
 
* A domain with '''hex mesh'''
 
* A domain with '''hex mesh'''
 
* '''snappyHexMeshDict''' located in the '''system''' sub-directory of''' case'''
 
* '''snappyHexMeshDict''' located in the '''system''' sub-directory of''' case'''
 
 
  
 
|-
 
|-
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* '''OpenFOAM''' version 2.2.1
 
* '''OpenFOAM''' version 2.2.1
 
* '''ParaView''' version 3.12.0
 
* '''ParaView''' version 3.12.0
 
 
  
 
|-
 
|-
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Type run '''cd OpenFOAM-2.2.2/tutorials/mesh/snappyHexMesh/flange'''
 
Type run '''cd OpenFOAM-2.2.2/tutorials/mesh/snappyHexMesh/flange'''
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| Let us learn, the different parameters in snappyHexMesh to generate mesh in OpenFOAM.
+
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| Let us learn, the different parameters in''' snappyHexMesh''' to generate '''mesh''' in '''OpenFOAM'''.
  
 
To do this, we will open the '''terminal window '''and enter the path for '''flange '''as shown.
 
To do this, we will open the '''terminal window '''and enter the path for '''flange '''as shown.
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|-
 
|-
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| Type '''ls'''
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| Type '''ls'''
 
 
  
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| Now type '''ls''' and press '''Enter.'''
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| Now type '''ls''' and press '''Enter.'''
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|-
 
|-
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| Type '''gedit snappyHexMeshDict'''
+
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| Type '''gedit space snappyHexMeshDict'''
 +
 
 +
(Note that H, M and D here are in capital letters.)
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| To view the contents of the file type -
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| To view the contents of the file type -
  
'''gedit snappyHexMeshDict '''
+
'''gedit space snappyHexMeshDict '''
  
 
and press '''Enter.'''
 
and press '''Enter.'''
 
 
(Note that H, M and D here are in capital letters.)
 
  
 
|-
 
|-
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|-
 
|-
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| '''nCellsBetweenLevels'''
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| '''nCellsBetweenLevels'''
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| '''nCellsBetweenLevels''' defines number of cells for each refinement level.  
+
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| '''nCellsBetweenLevels''' defines number of cells for each '''refinement level'''.  
  
  
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|-
 
|-
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| Explicit feature edge refinement
+
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| Highlight '''Explicit feature edge refinement'''
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| In the explicit feature edge refinement section, you can set specific refinement level for geometry’s feature edges.
+
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| In the '''Explicit feature edge refinement''' section, you can set specific '''refinement level''' for geometry’s feature edges.
  
  
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| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| In the '''surface-based refinement '''section, you can set the refinement levels of all surfaces defined in '''geometry''' file.
+
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| In the '''Surface-based refinement '''section, you can set the '''refinement levels''' of all surfaces defined in '''geometry''' file.
  
 
|-
 
|-
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| Mesh selection
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| Mesh selection
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| Mesh selection is a very important parameter.
+
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| '''Mesh selection''' is a very important parameter.
  
  
If the chosen point is inside the surface described in '''geometry''' file, then '''snappyHexMesh''' will create the internal mesh.
+
If the chosen point is inside the surface described in '''geometry''' file, then '''snappyHexMesh''' will create the internal '''mesh'''.
  
  
Otherwise the external part (inside the blockMesh) is meshed.
+
Otherwise the external part (inside the '''blockMesh''') is meshed.
  
 
|-
 
|-
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"|  
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"|  
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| The next step involves moving cell vertex points onto the surface geometry.
+
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| The next step involves moving '''cell vertex points''' onto the '''surface geometry'''.
  
 
|-
 
|-
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| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| The snapping process is carried out by four parameters:
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| The snapping process is carried out by four parameters:
  
* nSmoothPatch
+
* '''nSmoothPatch'''
* tolerance
+
* '''tolerance'''
* nSolveIter
+
* '''nSolveIter'''
* nRelaxIter
+
* '''nRelaxIter'''
  
 
These parameters control the number of iterations and tolerance between '''mesh''' and '''STL''' surface.
 
These parameters control the number of iterations and tolerance between '''mesh''' and '''STL''' surface.
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|-
 
|-
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| nSmoothPatch
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| nSmoothPatch
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| Modified sentence is shown in the script.
+
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| '''nSmoothPatch '''option changes how many times the exterior (the boundary wall) should be iterated.
  
  
Original sentence:
+
The '''mesh''' will become smoother if the number of iterations are more.
 
+
 
+
'''nSmoothPatch '''option changes how many times the exterior (the boundary wall) should be iterated.'''nSmoothPatch '''option changes how many times the exterior (the boundary wall) should be iterated.
+
 
+
 
+
The mesh will become smoother if the number of iterations are more.
+
  
 
|-
 
|-
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| tolerance
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| tolerance
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| Modified sentence is shown in the script.
+
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| '''Tolerance''' option changes how long distance the program should look for a point to snap.
 
+
 
+
Original sentence:
+
 
+
'''Tolerance''' option changes how long distance the program should look for a point to snap.'''Tolerance''' option changes how long distance the program should look for a point to snap.
+
  
  
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|-
 
|-
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| nSolveIter
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| nSolveIter
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| Modified Sentence'''nSolveIter '''option changes how many times the snapping part of '''snappyHexMesh '''should be run.
+
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| '''nSolveIter '''option changes how many times the snapping part of '''snappyHexMesh '''should be run.
  
 
|-
 
|-
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| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| Modified Sentence'''nRelaxIter''' option changes how many times the mesh should run a relaxing script, that removes bad mesh points.
+
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| '''nRelaxIter''' option changes how many times the mesh should run a relaxing script, that removes bad '''mesh''' points.
  
 
|-
 
|-
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| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| The process of mesh layer addition involves shrinking the existing mesh from the boundary and inserting layers of cells.
+
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| The process of '''mesh''' layer addition involves shrinking the existing '''mesh''' from the boundary and inserting layers of cells.
  
 
The group of parameters define the dimensions for layers and surface on which they will be attached.
 
The group of parameters define the dimensions for layers and surface on which they will be attached.
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|-
 
|-
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| layers
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"| layers
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| In '''layers''' option, you can define the number of '''layers''' and the patch on which attach the '''layers'''.
+
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| In '''layers''' option, you can define the number of '''layers''' and patch on which attach the '''layers'''.
  
  
It must be an STL patch in '''geomery''' menu, and not a user defined region.
+
It must be an STL patch in '''geometry''' menu, and not a user defined region.
  
 
|-
 
|-
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| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| '''ExpansionRatio''' parameters set the ratio between two subsequent layers.
+
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| '''ExpansionRatio''' parameters sets the ratio between two subsequent layers.
  
 
|-
 
|-
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| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| meshQualityControls parameter sets the minimum thresholds to generate mesh in snap and add-layers parts.
+
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| meshQualityControls parameter sets the minimum thresholds to generate mesh in '''snap''' and '''add-layers''' parts.
  
  
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But sometimes you can deactivate one or more controls to force mesh generation.
+
But sometimes, you can deactivate one or more controls to force '''mesh''' generation.
  
 
|-
 
|-
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"|  
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"|  
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| These are the different parameters in '''snappyHexMeshDict'''.
+
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| These are the different parameters in '''snappyHexMeshDict''' file.
  
  
 
These parameters are important to generate mesh using '''snappyHexMesh''' utility.
 
These parameters are important to generate mesh using '''snappyHexMesh''' utility.
  
|-
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.097cm;"|
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| <nowiki><PAUSE></nowiki>
 
 
Let me get back to the slides.
 
  
 
|-
 
|-
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| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| In this tutorial we learnt :
 
| style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:0.05pt solid #000000;padding:0.097cm;"| In this tutorial we learnt :
  
Different parameteres in '''snappyHexMesh '''to generate mesh in '''OpenFoam'''.
+
Different parameteres in '''snappyHexMesh '''to generate '''mesh''' in '''OpenFoam'''.
  
 
|-
 
|-

Revision as of 22:45, 5 July 2014

Tutorial: Introduction to snappyHexMesh in OpenFOAM.


Script and Narration: Chaitrali Ghodke.


Keywords: Import STL file, background hex mesh, snappyHexMeshDict.


Visual Cue
Narration
Slide 1 Hello and welcome to the spoken tutorial on Introduction to snappyHexMesh in OpenFOAM.
Slide 2 : Learning Objectives In this tutorial, we will learn about
  • The different parameters in snappyHexMesh to generate Mesh in OpenFOAM.
Slide 2: Pre-requisite As a pre-requisite, the user requires
  • Surface data files in STL format
  • A domain with hex mesh
  • snappyHexMeshDict located in the system sub-directory of case
Slide 3:

System Requirement

To record this tutorial, I am using
  • Ubuntu Linux operating system 12.04
  • OpenFOAM version 2.2.1
  • ParaView version 3.12.0
Slide 4: Methodology for snappyHexMesh


There are five steps to create a mesh with the snappyHexMesh utility.

Step 1 : Create a base mesh by using blockMesh utility

Step 2 : Refine base mesh

Step 3 : Remove unused cells

Step 4 : Snap mesh to surface

Step 5 : Add layers

Ctrl+Alt+t simultaneously

Type run cd OpenFOAM-2.2.2/tutorials/mesh/snappyHexMesh/flange

Let us learn, the different parameters in snappyHexMesh to generate mesh in OpenFOAM.

To do this, we will open the terminal window and enter the path for flange as shown.

Type run Type run and press Enter.
Type cd tutorials/mesh/snappyHexMesh/flange Type cd tutorials/mesh/snappyHexMesh/flange and press Enter.
Type ls Now type ls and press Enter.


There are two folders constant and system.

Type cd system Type cd space system and press Enter.
Type ls Now type ls and press Enter.


You can see the snappyHexMeshDict file.

Type gedit space snappyHexMeshDict

(Note that H, M and D here are in capital letters.)

To view the contents of the file type -

gedit space snappyHexMeshDict

and press Enter.

This will open up the snappyHexMeshDict file.
Let me drag this to the capture area.
Slide 5 : snappyHexMeshDict file contains all the instructions and the entire process revolves around this file.
Activation rows


With the first rows of snappyHexMeshDict, you can activate or skip sections of the process.
Geometry In geometry section, all active regions that take part in snappy process can be defined.
castellatedMeshControls section. The parameters that govern the process of cell splitting are described in castellatedMeshControls section.
CastellatedMeshControls The parameters that are listed below are well explained in snappyHexMeshDict file.
nCellsBetweenLevels nCellsBetweenLevels defines number of cells for each refinement level.


The higher it is, the more gradual the mesh will be.

Highlight Explicit feature edge refinement In the Explicit feature edge refinement section, you can set specific refinement level for geometry’s feature edges.


The .eMesh file can be obtained with the surfaceFeatureExtract utility.

Surface based refinement


In the Surface-based refinement section, you can set the refinement levels of all surfaces defined in geometry file.
Mesh selection Mesh selection is a very important parameter.


If the chosen point is inside the surface described in geometry file, then snappyHexMesh will create the internal mesh.


Otherwise the external part (inside the blockMesh) is meshed.

The next step involves moving cell vertex points onto the surface geometry.
SnapControls


Settings for the snapping


The snapping process is carried out by four parameters:
  • nSmoothPatch
  • tolerance
  • nSolveIter
  • nRelaxIter

These parameters control the number of iterations and tolerance between mesh and STL surface.

nSmoothPatch nSmoothPatch option changes how many times the exterior (the boundary wall) should be iterated.


The mesh will become smoother if the number of iterations are more.

tolerance Tolerance option changes how long distance the program should look for a point to snap.


The distance will be the number that is in tolerance.

nSolveIter nSolveIter option changes how many times the snapping part of snappyHexMesh should be run.
nRelaxIter


nRelaxIter option changes how many times the mesh should run a relaxing script, that removes bad mesh points.
addLayerControls


The process of mesh layer addition involves shrinking the existing mesh from the boundary and inserting layers of cells.

The group of parameters define the dimensions for layers and surface on which they will be attached.

relativeSizes RelativeSizes option (true or false) changes the way to read the parameters.
layers In layers option, you can define the number of layers and patch on which attach the layers.


It must be an STL patch in geometry menu, and not a user defined region.

expansionRatio


ExpansionRatio parameters sets the ratio between two subsequent layers.
finalLayerThickness


FinalLayerThickness parameter sets the thickness of the last layer.
minThickness MinThickness parameter sets the minimum allowable thickness of layer.
Advanced settings


Advanced settings is the second group of parameters.


It contains more specific controls that can help in layer creation.

featureAngle


FeatureAngle is the angle above which the surface will not be extruded.
==== nRelaxIter ==== nRelaxIter option changes how many times the mesh will run a relaxing script.
==== maxFaceThicknessRatio ==== MaxFaceThicknessRatio option changes the maximum allowable value of aspect ratio.
meshQualityControls


meshQualityControls parameter sets the minimum thresholds to generate mesh in snap and add-layers parts.


In 99% of the cases, it is better to leave the default values.


But sometimes, you can deactivate one or more controls to force mesh generation.

These are the different parameters in snappyHexMeshDict file.


These parameters are important to generate mesh using snappyHexMesh utility.


Let us summarize.
Slide 9: Summary


In this tutorial we learnt :

Different parameteres in snappyHexMesh to generate mesh in OpenFoam.

Slide 10: About Spoken tutorials Watch the video available at this URL:

http://spoken-tutorial.org/What_is_a_Spoken_Tutorial

It summarizes the Spoken Tutorial project.

If you do not have good bandwidth, you can download and watch it.

Slide 11:

About Spoken tutorials

The Spoken Tutorial Project Team

-Conducts workshops using spoken tutorials

-Gives certificates to those who pass an online test

-For more details, please write to

contact@spoken-tutorial.org

Slide 12:

Acknowledgement


Spoken Tutorial is a part of Talk to a Teacher project,

It is supported by the National Mission on Education through ICT, MHRD, Government of India.

More information on the same is available at the following URL link http://spoken-tutorial.org/NMEICT-Intro

About the contributor This is Chaitrali Ghodke from IIT BOMBAY signing off.

Thanks for joining.

Contributors and Content Editors

Chaitralighodke, Nancyvarkey