Difference between revisions of "Anisotropic Mesh Generation"

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==AFLR==
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== Analytic Metric Functions ==
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==CDT3D==
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===Linear metric===
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=== Analytic Metric Functions ===
 
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* Linear metric given by  [[File:Linear metric.png| 300px]]
 
  
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Metric given by  [[File:Linear metric.png| 300px|link=]]
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where h<sub>x</sub> =0.1, h<sub>y</sub>=0.1, h<sub>0</sub> = 0.001, h<sub>z</sub> = h<sub>0</sub> + 2(0.1-h<sub>0</sub>)|z-0.6|
  
 
{|
 
{|
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!colspan="2"| Surface Mesh, cross-cut and detail of the generated volume mesh.
 
!colspan="2"| Surface Mesh, cross-cut and detail of the generated volume mesh.
 
|}
 
|}
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{|
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|-
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|[[File:Cube_qcircle_edges.png|350px]]
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|[[File:Cube_qcircle_qual.png|350px]]
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|-
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!colspan="2"| Quality statistics in the metric space for generated volume mesh.94 % of the edges has length between [0.5,1.5].
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For the mean ratio 96%,of the elements have quality higher that 0.7.
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|}
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=== Quarter of a Cylinder ===
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Metric given by [[File:Qcircle_metric.png| 700px]]
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where h<sub>x</sub> = min(0.002  5^a, h<sub>max</sub>),
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h<sub>y</sub> = min(0.05 &middot; 2<sup>a</sup>, h<sub>max</sub>),
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h<sub>z</sub>= h<sub>max</sub>,
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h<sub>max</sub> = 0.1,
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θ = arctan(x,y),
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a = 10 &middot; | 0.75 -
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<!-- code for square root -->
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&radic;<span style="text-decoration:overline">
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(<i>x</i><span style="font-size: 10px;vertical-align:+25%;">2</span>+
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<i>y</i><span style="font-size: 10px;vertical-align:+25%;">2</span>)&nbsp;</span>
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<!-- code for square root -->
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|
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{|
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|-
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|[[File:Cube_qcircle1.png|300px|link=]]
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|[[File:Cube_qcircle2.png|300px|link=]]
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|[[File:Cube_qcircle_detail.png|300px|link=]]
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|-
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!colspan="2"| Surface Mesh, cross-cut and detail of the generated volume mesh.
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|}
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{|
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|-
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|[[File:Cube_linear_edges.png|350px|link=]]
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|[[File:Cube_linear_qual.png|350px|link=]]
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|-
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!colspan="2"| Quality statistics in the metric space for generated volume mesh.
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91 % of the edges has length between [0.5,1.5]. For the mean ratio 79%
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of the elements have quality higher that 0.7.
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|}
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== Solution Based Adaptation ==
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=== Onera M6 ===
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==== 30K Complexity ====
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Surface and background meshes were acquired from [https://github.com/UGAWG UGAWG repository]
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{|
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|-
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|[[File:Onera_initial mesh.png|500px]]
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|[[File:RefinedSurface_onera03.png|500px]]
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|-
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| '''Initial surface mesh acquired from [https://github.com/UGAWG/solution-adapt-cases/blob/master/onera-m6/initial-grid/onera_curvAdapt.meshb]'''
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| '''Refined surface mesh using as a 30K complexity background mesh acquired from [https://github.com/UGAWG/solution-adapt-results/blob/master/onera-m6/sa-m084-a306-fun3d/onera03-metric.solb]'''
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|-
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| [[File:Onera03_side.png|500px]]
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| [[File:Onera03_cross_section.png|500px]]
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|-
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| colspan="2" style="text-align: center;" | ''' cross cuts of the final mesh'''
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|}
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The final mesh (available [http://cs.odu.edu/crtc/CDT3D/Anisotropic/onera03_CDT3D.7z here] ) was compared against the results from the 2018 Scitech paper ''' Unstructured Grid Adaptation and Solver Technology for Turbulent Flows'''
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available at https://arc.aiaa.org/doi/abs/10.2514/6.2018-1103 .
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{|
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|-
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|[[File:Histogram ratio onera03.png|500px]]
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|[[File:Histogram qual onera03.png|500px]]
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|-
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|}
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==== 50K Complexity ====
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Same input surface but with different metric complexity :
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{|
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| [[File:Onera05_side.png|500px]]
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| [[File:Onera05_cross_section.png|500px]]
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|-
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| colspan="2" style="text-align: center;" | ''' cross cuts of the final mesh'''
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|}
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The background mesh is available [https://github.com/UGAWG/solution-adapt-results/blob/master/onera-m6/euler-m084-a306-fun3d/onera05-metric.solb here ]
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The final mesh (available [http://cs.odu.edu/crtc/CDT3D/Anisotropic/onera05_CDT3D.7z here] )

Latest revision as of 14:56, 13 April 2018

Analytic Metric Functions

Linear metric

Metric given by Linear metric.png where hx =0.1, hy=0.1, h0 = 0.001, hz = h0 + 2(0.1-h0)|z-0.6|

Cube linear.png Cube linear2.png Cube linear detail.png
Surface Mesh, cross-cut and detail of the generated volume mesh.
Cube qcircle edges.png Cube qcircle qual.png
Quality statistics in the metric space for generated volume mesh.94 % of the edges has length between [0.5,1.5].

For the mean ratio 96%,of the elements have quality higher that 0.7.

Quarter of a Cylinder

Metric given by Qcircle metric.png

where hx = min(0.002 5^a, hmax), hy = min(0.05 · 2a, hmax), hz= hmax, hmax = 0.1, θ = arctan(x,y), a = 10 · | 0.75 - √ (x2+ y2)  |

Cube qcircle1.png Cube qcircle2.png Cube qcircle detail.png
Surface Mesh, cross-cut and detail of the generated volume mesh.
Cube linear edges.png Cube linear qual.png
Quality statistics in the metric space for generated volume mesh.

91 % of the edges has length between [0.5,1.5]. For the mean ratio 79% of the elements have quality higher that 0.7.


Solution Based Adaptation

Onera M6

30K Complexity

Surface and background meshes were acquired from UGAWG repository

Onera initial mesh.png RefinedSurface onera03.png
Initial surface mesh acquired from [1] Refined surface mesh using as a 30K complexity background mesh acquired from [2]
Onera03 side.png Onera03 cross section.png
cross cuts of the final mesh


The final mesh (available here ) was compared against the results from the 2018 Scitech paper Unstructured Grid Adaptation and Solver Technology for Turbulent Flows available at https://arc.aiaa.org/doi/abs/10.2514/6.2018-1103 .

Histogram ratio onera03.png Histogram qual onera03.png

50K Complexity

Same input surface but with different metric complexity :

Onera05 side.png Onera05 cross section.png
cross cuts of the final mesh

The background mesh is available here

The final mesh (available here )

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