Isotropic Mesh Generation

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.

nacelle, rocket, and lv2b pg. 122-124

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
Nacelle	CDT3D	0.291	0.7	2	3	0.5	1	2	165°	120°
	AFLR	0.50	0.7	2	3	0.5	1	2	165°	120°
Rocket	CDT3D	0.20	0.7	2	3	0.5	1	2	165°	120°
	AFLR	0.60	0.7	2	3	0.5	1	2	165°	120°
Lv2b	CDT3D	0.234	0.7	2	3	0.5	1	2	165°	120°
	AFLR	0.30	0.7	2	3	0.5	1	2	165°	120°

**(WORK IN PROGRESS)**Evaluation results on unstructured grid generation. CDT3D is compared with state-of-the-art technology AFLR v 16.9.19 [132]. CDT3D's runs are performed with 1 and 12 hardware cores. AFLR is a sequential code. Table 18 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 were performed on a Dell workstation with Linux Ubuntu 12.10, a 12-core Intel Xeon X5690@3.47 GHz CPU, and 96 GB RAM.
		%Slivers (w/o improv.) (x10^-3)		#Tets (w/ improv.) (M)		Min/Max Angle (w/ improv.) (deg)		Time
Case	Software		#Cores				1261		3860		9644
#edges	8340		4158		8433		3921		11574		28926
#faces	5560		2772		5622		2614		7716		19284
Software	TetGen	CDT3D	TetGen	CDT3D	TetGen	CDT3D	TetGen	CDT3D	TetGen	CDT3D	TetGen	CDT3D
#Stpts (boundary)	0	0	0	0	0	0	1	0	-	0	0	0
#Stpts (volume)	7	2	0	0	8	5	59	28	-	0	0	0
Time (sec)	0.18	0.29	0.08	0.11	0.11	0.09	0.18	2.6	-	0.36	0.02	0.20