Difference between revisions of "Isotropic Mesh Generation"

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(→‎nacelle, rocket, and lv2b pg. 122-124)
(→‎more nacelle, rocket, and lv2b pg. 125-127)
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== more nacelle, rocket, and lv2b pg. 125-127 ==
 
== more nacelle, rocket, and lv2b pg. 125-127 ==
 
<div><ul>  
 
<div><ul>  
−
<li style="display: inline-block;"> [[File: nacelleCDT3D.png|thumb|none|850px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: nacelleCDT3D.png|thumb|none|750px|''(a) CDT3D: 42.85 M tetrahedra'']] </li>
−
<li style="display: inline-block;"> [[File: nacelleAFLR.png|thumb|none|850px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: nacelleAFLR.png|thumb|none|750px|''(b) AFLR: 39.64 M tetrahedra'']] </li>
 
</ul></div>
 
</ul></div>
 +
 +
:Tetrahedral field cuts of the aircraft nacelle
 +
<br><br><br>
  
 
<div><ul>  
 
<div><ul>  
−
<li style="display: inline-block;"> [[File: nacelle5_small.png|thumb|none|650px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: nacelle5_small.png|thumb|none|650px]] </li>
−
<li style="display: inline-block;"> [[File: nacelle9.png|thumb|none|650px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: nacelle9.png|thumb|none|650px]] </li>
 
</ul></div>
 
</ul></div>
 +
 +
:Detail views of tetrahedral field cuts of aircraft nacelle generated with CDT3D
 +
<br><br><br>
  
 
<div><ul>  
 
<div><ul>  
−
<li style="display: inline-block;"> [[File: rocketCDT3D.png|thumb|none|650px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: rocketCDT3D.png|thumb|none|650px|''(a) CDT3D: 119.06 M tetrahedra'']] </li>
−
<li style="display: inline-block;"> [[File: rocketAFLR.png|thumb|none|650px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: rocketAFLR.png|thumb|none|650px|''(b) AFLR: 127.68 M tetrahedra'']] </li>
 
</ul></div>
 
</ul></div>
−
 
 
<div><ul>  
 
<div><ul>  
−
<li style="display: inline-block;"> [[File: rocket5.png|thumb|none|650px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: rocket5.png|thumb|none|650px|''(c) Detail view of (a)'']] </li>
−
<li style="display: inline-block;"> [[File: rocket9.png|thumb|none|650px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: rocket9.png|thumb|none|650px|''(d) Detail view of (a)'']] </li>
 
</ul></div>
 
</ul></div>
 +
 +
:Tetrahedral field cuts of the rocket
 +
<br><br><br>
  
 
<div><ul>  
 
<div><ul>  
−
<li style="display: inline-block;"> [[File: lv2bCDT3D.png|thumb|none|650px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: lv2bCDT3D.png|thumb|none|650px|''(a) CDT3D: 110.01 M tetrahedra'']] </li>
−
<li style="display: inline-block;"> [[File: lv2bAFLR.png|thumb|none|650px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: lv2bAFLR.png|thumb|none|650px|''(b) AFLR: 100.92 M tetrahedra'']] </li>
 
</ul></div>
 
</ul></div>
−
 
 
<div><ul>  
 
<div><ul>  
−
<li style="display: inline-block;"> [[File: lv2b7.png|thumb|none|650px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: lv2b7.png|thumb|none|650px|''(c) Detail view of (a)'']] </li>
−
<li style="display: inline-block;"> [[File: lv2b8.png|thumb|none|650px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: lv2b8.png|thumb|none|650px|''(d) Detail view of (a)'']] </li>
 
</ul></div>
 
</ul></div>
  
 +
Tetrahedral field cuts of the Lv2b
 +
<br><br><br>
  
 
<div><ul>  
 
<div><ul>  
−
<li style="display: inline-block;"> [[File: histogramNacelleNoOpt.png|thumb|none|650px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: histogramNacelleNoOpt.png|thumb|none|650px|''(a) w/o improvement'']] </li>
−
<li style="display: inline-block;"> [[File: histogramNacelleOpt.png|thumb|none|650px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: histogramNacelleOpt.png|thumb|none|650px|''(b) w/ improvement'']] </li>
 
</ul></div>
 
</ul></div>
  
 +
Element angle distribution (in 5-deg increments) of aircraft nacelle grids. <br>The dihedral angle extrema are reported for each method.
 +
<br><br><br>
  
 
<div><ul>  
 
<div><ul>  
−
<li style="display: inline-block;"> [[File: histogramRocketOpt.png|thumb|none|650px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: histogramRocketOpt.png|thumb|none|650px|''(a) Rocket (w/ improvement)'']] </li>
−
<li style="display: inline-block;"> [[File: histogramLvOpt.png|thumb|none|650px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: histogramLvOpt.png|thumb|none|650px|''(b) Lv2b (w/ improvement)'']] </li>
 
</ul></div>
 
</ul></div>
  
 +
Element angle distribution (in 5-deg increments) after improvement of Rocket and Lv2b grids. <br>The dihedral angle extrema are reported for each method.
 +
<br><br><br>
  
 
<div><ul>  
 
<div><ul>  
−
<li style="display: inline-block;"> [[File: sliversNacelleCDT3D.png|thumb|none|650px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: sliversNacelleCDT3D.png|thumb|none|650px|''(a) CDT3D: 1590 slivers (0.0037%) out of total 42.91 M tetrahedra'']] </li>
−
<li style="display: inline-block;"> [[File: sliversNacelleAFLR.png|thumb|none|650px|''PLACEHOLDER'']] </li>
+
<li style="display: inline-block;"> [[File: sliversNacelleAFLR.png|thumb|none|650px|''(b) AFLR: 1287 slivers (0.0029%) out of total 43.23 M tetrahedra'']] </li>
 
</ul></div>
 
</ul></div>
 +
 +
Slivers after the completion of refinement of the aircraft nacelle. <br>Red represents elements whose minimum dihedral angle is smaller than 2◦ or larger than 178◦.
  
 
== aircraft pg. 140-142 ==
 
== aircraft pg. 140-142 ==

Revision as of 12:59, 27 March 2018

Sphere and Two Blades with Merging Wakes and a Symmetry Plane

  • (a) Input Surface
  • (b) cdfm: 0; #tets: 57K
  • (c) cdfm: 0.2; #tets: 58K
  • (d) cdfm: 0.6; #tets: 129K
  • (e) cdfm: 0.8; #tets: 854K
  • (f) cdfm: 0.9; #tets: 7.68M

Cuts of tetrahedral grids of a sphere generated for varied cdfm ∈ [0, 1]. Blue corresponds to larger values of the distribution function. Red corresponds to smaller values
of the distribution function.





  • (a) Input Surface
  • (b) Distribution function on the boundary
  • (c) cdfm: 0; #tets: 806K
  • (d) cdfm: 0.1; #tets: 1.41M
  • (e) cdfm: 0.2; #tets: 4.97M
  • (f) cdfm: 0.3; #tets: 16.54M

Cuts of tetrahedral grids of two blades with merging wakes and a symmetry plane enclosed in an outer boundary generated for varied cdfm ∈ [0, 1] (shown in (c)-(f)).
The input surface is depicted in (a)-(b). The wake region is modeled as an embedded/ transparent delete surface.





  • Sphere histogram.png

Element angle distribution (in 5-deg increments) of grids of sphere, for varied cdfm.
The dihedral angle extrema and the element count are reported for each grid.



  • Blades histogram.png

Element angle distribution (in 5-deg increments) of grids of two blades with
merging wakes and a symmetry plane enclosed in an outer boundary, for varied cdfm.
The dihedral angle extrema and the element count are reported for each grid.

nacelle, rocket, and lv2b pg. 122-124

  • Nacelle6.png
  • Nacelle7.png
  • Nacelle8.png
Surface grid of an aircraft nacelle with engine inside a section of wind tunnel.
#points: 27184; #triangles: 54360




  • Rocket8.png
  • Rocket6.png
Surface grid of a rocket with engine, nozzle and transparent internal data surfaces inside flow field.
#points: 20228; #triangles: 40448




  • Lv2b2.png
  • Lv2b6.png
Surface grid of a launch vehicle with solid boosters inside flow field (Lv2b).
#points: 42020; #triangles: 84024




Parameters for unstructured grid generation. Additional parameters only for CDT3D: nthreads : 12 (parallel); nthreads : 1 (sequential); nbuckets : 240; frbtransf : 0.3; cbtransf : 1.0. Additional parameters only for AFLR: mrecrbf : 0.
Geometry Software cdfm cdfn mrecm nqual csmth msmth nsmth angdfs angqual mdbs
Nacelle CDT3D 0.291 0.7 2 3 0.5 1 2 165° 120° 0
AFLR 0.50 0.7 2 3 0.5 1 2 165° 120° 0
Rocket CDT3D 0.20 0.7 2 3 0.5 1 2 165° 120° 0
AFLR 0.60 0.7 2 3 0.5 1 2 165° 120° 0
Lv2b CDT3D 0.234 0.7 2 3 0.5 1 2 165° 120° 0
AFLR 0.30 0.7 2 3 0.5 1 2 165° 120° 0




Evaluation results on unstructured grid generation. CDT3D is compared with state-of-the-art technology AFLR v16.9.19 [132]. CDT3D’s runs are performed with 1 and 12 hardware cores. AFLR is a sequential code. Table 17 lists the parameters of the evaluation. The sliver elements have a dihedral angle smaller than 2◦ or larger than 178◦. Initial grid includes Delaunay tetrahedralization and Boundary Recovery. The I/O time is not included. The experiments performed on a DELL workstation with Linux Ubuntu 12.10, 12 cores Intel(R) Xeon(R) CPU X5690@3.47 GHz, and 96 GB RAM.
Case Software #Cores  %Slivers
(w/o improv.)
(x10-3) 		#Tets
(w/ improv.)(M) 		Min/Max Angle
(w/ improv.)
(deg) 		Initial Grid
(sec) 		Refinement
(min) 		Improvement
(min) 		Total
(min)
Nacelle CDT3D 1 3.74 43.65 13.57°/153.44° 1.36 20.01 14.30 34.33
CDT3D 12 3.70 42.85 12.06°/159.52° 1.36 5.02 18.59 23.64
AFLR 1 2.97 43.16 7.00°/164.86° 5.63 22.59 6.40 29.09
Rocket CDT3D 1 2.96 118.41 9.39°/159.30° 1.58 52.85 64.56 117.44
CDT3D 12 2.95 119.06 9.21°/158.33° 1.58 14.51 68.23 82.76
AFLR 1 3.05 123.13 5.58°/164.75° 6.76 131.89 25.41 157.42
Lv2b CDT3D 1 5.09 98.21 6.60°/159.68° 5.45 41.57 94.63 136.29
CDT3D 12 4.69 113.99 8.24°/158.59° 5.45 12.92 62.36 75.37
AFLR 1 3.49 104.10 6.84°/164.88° 16.97 98.24 18.51 117.03

more nacelle, rocket, and lv2b pg. 125-127

  • (a) CDT3D: 42.85 M tetrahedra
  • (b) AFLR: 39.64 M tetrahedra
Tetrahedral field cuts of the aircraft nacelle




  • Nacelle5 small.png
  • Nacelle9.png
Detail views of tetrahedral field cuts of aircraft nacelle generated with CDT3D




  • (a) CDT3D: 119.06 M tetrahedra
  • (b) AFLR: 127.68 M tetrahedra
  • (c) Detail view of (a)
  • (d) Detail view of (a)
Tetrahedral field cuts of the rocket




  • (a) CDT3D: 110.01 M tetrahedra
  • (b) AFLR: 100.92 M tetrahedra
  • (c) Detail view of (a)
  • (d) Detail view of (a)

Tetrahedral field cuts of the Lv2b


  • (a) w/o improvement
  • (b) w/ improvement

Element angle distribution (in 5-deg increments) of aircraft nacelle grids.
The dihedral angle extrema are reported for each method.


  • (a) Rocket (w/ improvement)
  • (b) Lv2b (w/ improvement)

Element angle distribution (in 5-deg increments) after improvement of Rocket and Lv2b grids.
The dihedral angle extrema are reported for each method.


  • (a) CDT3D: 1590 slivers (0.0037%) out of total 42.91 M tetrahedra
  • (b) AFLR: 1287 slivers (0.0029%) out of total 43.23 M tetrahedra

Slivers after the completion of refinement of the aircraft nacelle.
Red represents elements whose minimum dihedral angle is smaller than 2◦ or larger than 178◦.

aircraft pg. 140-142

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