Isotropic Mesh Generation

Refinement Results of 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.

• 

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.

• 

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.

Surface Meshes and Parameters Used to Refine Nacelle Engine, Rocket, and Launch Vehicle with Two Boosters (lv2b)

• 

• 

• 

Surface grid of an aircraft nacelle with engine inside a section of wind tunnel.

#points: 27184; #triangles: 54360

• 

• 

Surface grid of a rocket with engine, nozzle and transparent internal data surfaces inside flow field.

#points: 20228; #triangles: 40448

• 

• 

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

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

• 

  (a) CDT3D: 42.85 M tetrahedra

• 

  (b) AFLR: 39.64 M tetrahedra

Tetrahedral field cuts of the aircraft nacelle

• 

• 

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◦.