Isotropic Mesh Generation

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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