Isotropic Mesh Generation

Sphere and Two Blades with Merging Wakes and a Symmetry Plane

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  (a) Input Surface
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  (b) cdfm: 0; #tets: 57K

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  (c) cdfm: 0.2; #tets: 58K
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  (d) cdfm: 0.6; #tets: 129K

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  (e) cdfm: 0.8; #tets: 854K
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  (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.

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  (a) Input Surface
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  (b) Distribution function on the boundary

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  (c) cdfm: 0; #tets: 806K
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  (d) cdfm: 0.1; #tets: 1.41M

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  (e) cdfm: 0.2; #tets: 4.97M
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  (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.

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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.

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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

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

#points: 27184; #triangles: 54360

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

#points: 20228; #triangles: 40448

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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

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  (a) CDT3D: 42.85 M tetrahedra
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  (b) AFLR: 39.64 M tetrahedra

Tetrahedral field cuts of the aircraft nacelle

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Detail views of tetrahedral field cuts of aircraft nacelle generated with CDT3D

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  (a) CDT3D: 119.06 M tetrahedra
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  (b) AFLR: 127.68 M tetrahedra

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  (c) Detail view of (a)
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  (d) Detail view of (a)

Tetrahedral field cuts of the rocket

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  (a) CDT3D: 110.01 M tetrahedra
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  (b) AFLR: 100.92 M tetrahedra

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  (c) Detail view of (a)
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  (d) Detail view of (a)

Tetrahedral field cuts of the Lv2b

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

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

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  (a) Rocket (w/ improvement)
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  (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.

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  (a) CDT3D: 1590 slivers (0.0037%) out of total 42.91 M tetrahedra
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  (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◦.