Difference between revisions of "Isotropic Mesh Generation"

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(separate two examples for easier navigation, decrease size of spheres)
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== Refinement of Sphere and Two Blades with Merging Wakes and a Symmetry Plane ==
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== Sphere ==
  
 
<div><ul>  
 
<div><ul>  
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<li style="display: inline-block;"> [[File: sphere-eps-converted-to.png|thumb|none|450px|'''(a) Input Surface''']] </li>
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<li style="display: inline-block;"> [[File: sphere-eps-converted-to.png|thumb|none|350px|'''(a) Input Surface''']] </li>
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<li style="display: inline-block;"> [[File: sphere_cdfm0-eps-converted-to.png|thumb|none|450px|'''(b) cdfm: 0; #tets: 57K''']] </li>
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<li style="display: inline-block;"> [[File: sphere_cdfm0-eps-converted-to.png|thumb|none|350px|'''(b) cdfm: 0; #tets: 57K''']] </li>
 
</ul></div>
 
</ul></div>
  
 
<div><ul>  
 
<div><ul>  
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<li style="display: inline-block;"> [[File: sphere_cdfm0_2-eps-converted-to.png|thumb|none|450px|'''(c) cdfm: 0.2; #tets: 58K''']] </li>
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<li style="display: inline-block;"> [[File: sphere_cdfm0_2-eps-converted-to.png|thumb|none|350px|'''(c) cdfm: 0.2; #tets: 58K''']] </li>
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<li style="display: inline-block;"> [[File: sphere_cdfm0_6-eps-converted-to.png|thumb|none|450px|'''(d) cdfm: 0.6; #tets: 129K''']] </li>
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<li style="display: inline-block;"> [[File: sphere_cdfm0_6-eps-converted-to.png|thumb|none|350px|'''(d) cdfm: 0.6; #tets: 129K''']] </li>
 
</ul></div>
 
</ul></div>
  
 
<div><ul>  
 
<div><ul>  
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<li style="display: inline-block;"> [[File: sphere_cdfm0_8-eps-converted-to_s.png|thumb|none|450px|'''(e) cdfm: 0.8; #tets: 854K''']] </li>
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<li style="display: inline-block;"> [[File: sphere_cdfm0_8-eps-converted-to_s.png|thumb|none|350px|'''(e) cdfm: 0.8; #tets: 854K''']] </li>
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<li style="display: inline-block;"> [[File: sphere_cdfm0_9-eps-converted-to.png|thumb|none|450px|'''(f) cdfm: 0.9; #tets: 7.68M''']] </li>
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<li style="display: inline-block;"> [[File: sphere_cdfm0_9-eps-converted-to.png|thumb|none|350px|'''(f) cdfm: 0.9; #tets: 7.68M''']] </li>
 
</ul></div>
 
</ul></div>
  
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corresponds to larger values of the distribution function. Red corresponds to smaller values<br>
 
corresponds to larger values of the distribution function. Red corresponds to smaller values<br>
 
of the distribution function.
 
of the distribution function.
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<br><br><br><br><br><br>
 
  
 +
<div><ul>
 +
<li style="display: inline-block;"> [[File: sphere_histogram.png|thumb|none|2000px]] </li>
 +
</ul></div>
 +
 +
Element angle distribution (in 5-deg increments) of grids of sphere, for varied
 +
cdfm.<br> The dihedral angle extrema and the element count are reported for each grid.
 +
 +
==  Two Blades with Merging Wakes and a Symmetry Plane ==
 
<div><ul>  
 
<div><ul>  
 
<li style="display: inline-block;"> [[File: blades-eps-converted-to.png|thumb|none|450px|'''(a) Input Surface''']] </li>
 
<li style="display: inline-block;"> [[File: blades-eps-converted-to.png|thumb|none|450px|'''(a) Input Surface''']] </li>
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(c)-(f)). <br>The input surface is depicted in (a)-(b). The wake region is modeled as an embedded/
 
(c)-(f)). <br>The input surface is depicted in (a)-(b). The wake region is modeled as an embedded/
 
transparent delete surface.
 
transparent delete surface.
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<br><br><br><br><br><br>
 
  
−
<div><ul>
 
−
<li style="display: inline-block;"> [[File: sphere_histogram.png|thumb|none|2000px]] </li>
 
−
</ul></div>
 
−
 
−
Element angle distribution (in 5-deg increments) of grids of sphere, for varied
 
−
cdfm.<br> The dihedral angle extrema and the element count are reported for each grid.
 
−
<br><br><br><br>
 
 
<div><ul>  
 
<div><ul>  
 
<li style="display: inline-block;"> [[File: blades_histogram.png|thumb|none|2000px]] </li>
 
<li style="display: inline-block;"> [[File: blades_histogram.png|thumb|none|2000px]] </li>

Revision as of 04:44, 28 March 2018

Sphere

  • (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.

  • 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.

Two Blades with Merging Wakes and a Symmetry Plane

  • (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.

  • 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.

Refinement of Nacelle Engine, Rocket, and Launch Vehicle with Two Boosters (lv2b)

  • 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. CDT3D’s runs are performed with 1 and 12 hardware cores. AFLR is a sequential code. This table lists the parameters of the evaluation. The sliver elements have a dihedral angle smaller than 2° or larger than 178°. The initial grid includes Delaunay tetrahedralization and Boundary Recovery. The I/O time is not included. The experiments were performed on a Dell workstation with Linux Ubuntu 12.10, using a 12-core Intel Xeon 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




  • (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◦.

Refinement of DLR-F6 Airbus type aircraft

  • (a) Aircraft with symmetry plane
  • (b) Surface grid
  • (c) Wing-nacelle-pylon system
  • (d) Anisotropic boundary layers
Surface grid of a DLR-F6 Airbus type aircraft with anisotropic boundary layers on a symmetry plane;
#points: 1006144; #triangles: 2012288




  • (a) Overall view
  • (b) Detail view
Cuts of the tetrahedral grid of the flow field of DLR-F6 Airbus aircraft, generated with CDT3D. A smaller grid (≈200 M tetrahedra) is depicted due to limitations in visualization.




Performance results on parallel refinement of grid of a flow domain around a DLR-F6 Airbus aircraft. Parameters: cdfn : 0.8; cdfm : 0.5; mrecm : 2; mrec4 : 1; nbuckets : 15 · nthreads; frbtransf : 0.4; cbtransf : 1.0; nqual : 0; sortp : 1 activates element sorting. The included sorting time is reported in parenthesis. The sliver elements have a dihedral angle smaller than 2◦ or larger than 178◦. #Iter is the number of grid generation passes. The experiments performed on a DELL workstation with Linux Red Hat Enterprise, 24 hardware cores Intel(R) Xeon(R) CPU E5-2697v2@2.70 GHz, and 757 GB RAM. Hyper-Threading is enabled when nthreads > 24.
nthreads #Tets
(Bi) 		 %Slivers
(w/o improv.)
(x10-2) 		#Iter Recon./Iter
(min) 		Refinement
(hours) 		Recon./Iter
(Speedup) 		Refinement
(Speedup)
1 1.414 1.438 61 51.69 58.98 1 1
w/o sorting 12 1.413 1.472 73 4.81 13.10 10.74 4.50
24 1.455 1.563 83 2.51 11.81 20.59 5.00
36 1.438 1.487 79 1.98 10.59 26.10 5.57
48 1.451 1.556 118 1.84 14.36 28.09 4.10
w/ sorting 12 1.414 1.563 89 3.99 17.38 (3.62) 12.95 3.39
24 1.439 1.499 75 1.98 12.74 (3.16) 26.10 4.62
36 1.458 1.518 93 1.67 14.87 (4.00) 30.95 3.96
48 1.448 1.625 122 1.39 18.77 (5.08) 37.18 3.14



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