From this study, future work is summarized as follows:
1. From performance test, we can see that there is a bottleneck need to overcome.
2. Test with PDSC for more case or with other module to solve other problems.
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Table 1 Timing (seconds) for different processor numbers
(Surface mesh for a single jet case, original mesh: cells:997,421. nodes: 190,052.
level-1 refinement: cells:5,522,029. nodes:985,295.)
Processor NO. 2 4 8 16
Preprocessing 15.988 18.485 20.077 17.602
I 1564.7 499.08 659.9 491.86
II 14295 5360.4 5149.8 6922.2
III 1.35 2.072 2.174 2.399
IV 44.07 23.338 15.961 10.585 I. Add nodes on cell edges
II. Renumber added nodes III. Update connectivity data IV. Build neighbor identifier array
Table 2 Different refined level mesh for a hypersonic flow over 70o blunt cone with attack angle of 100. (Kn=0.0108)
Angle of Attack 10o (1/2 domain)
Level Cell No. Node No. Sim. Particle No.
0 15,190 3,573 16,808
1 46,817 9,550 42,120
2 270,382 49,222 390,794
3 1,117,241 195,879 3,697,429
Table 3 Comparison between experimental data and simulation data for different refined level mesh for a hypersonic flow over 70o blunt cone with attack angle of 100. (Kn=0.0108)
Angle of Attack 10o
Level Cd Cl Cm
0 1.688(14.36%) -0.135(25.00%) -0.064(18.52%)
1 1.652(11.92%) -0.147(18.33%) -0.063(16.67%)
2 1.587(7.52%) -0.163(9.44%) -0.058(7.41%)
3 1.555(5.35%) -0.175(2.78%) -0.055(1.85%)
Exp. Data 1.476 -0.18 -0.054
Figure 1 Isotropic mesh refinement of tetrahedral mesh. (T: Tetrahedron )
isotropic ( 1st stage) isotropic ( 2nd stage)
anisotropic ( 2nd stage) initial grid
initial grid
initial grid
2 hanging node anisotropic (2nd stage)
3 hanging node isotropic (2nd stage)
1 hanging node anisotropic (2nd stage)
2 hanging node
3 hanging node 1 hanging node
Figure 2 Mesh refinement rules for two-dimensional triangular cell
refined 4 cells
refined 8 cells refined 2 cells
(+1) (+2) (+3) (+1) (+4)
non-coplanar coplanar
6 5 4 3 2 1
coplanar
: n hanging node (+n) : adding n nodes
n
Figure 3 Schematic diagram for mesh refinement rules of tetrahedron
quality control no quality control
refined 2 cells
Figure 4 Schematic diagram of the proposed cell quality control
Figure 5 Schematic diagram of typical of cell quality control
quality control no quality control
refined 2 cells
Figure 6 Schematic diagram of simple cell quality control by Wu et al. [2004a]
Figure 7 A case that the proposed cell-quality-control would not affect to it
read grid data &
refine all cells by refinement criteria
Figure 8 Simplified flow chart of the serial mesh refinement.
Figure 9 Flow chart of parallel mesh refinement module
CPU0 gather output data
flag the cells based on refinement criteria
renumber added nodes
synchronize
stop start
add nodes on cell edge refinement required
Figure 10 Flow chart of module I (add nodes on cell edges)
remove hanging nodes
stop start
add nodes on isotropic cells
communicate hanging node information
hanging nodes on IPB
?
yes
no
add nodes on anisotropic cells
Figure 11 Flow chart of serial DSMC method
Average samples and print out the data index particles
Figure 12 Simplified flow chart of the parallel DSMC method (PDSC)
Figure 13 Coupled PDSC-PAMR Method
(weighting based on cell volume)
start
Figure 14 Sketch of a hypersonic flow over 70o blunt cone N2
M∞ = 20 T∞ = 13.6 K
Tw = 300 K α=1
α
Figure 15 Original mesh of a hypersonic flow over 70o blunt cone with attack angle of 100.
Figure 16 Level 1 refined mesh of a hypersonic flow over 70o blunt cone with attack angle of 100.
Figure 17 Level 2 refined mesh of a hypersonic flow over 70o blunt cone with attack angle of 100.
Figure 18 Level 3 refined mesh of a hypersonic flow over 70o blunt cone with attack angle of 100.
Figure 19 Normalized density of original mesh of a hypersonic flow over 70o blunt cone with attack angle of 100. (Kn=0.0108)
Figure 20 Normalized temperature of original mesh of a hypersonic flow over 70o blunt cone with attack angle of 100. (Kn=0.0108)
Figure 21 Streamlines of original mesh of a hypersonic flow over 70o blunt cone with attack angle of 100. (Kn=0.0108)
Figure 22 Mach number of original mesh of a hypersonic flow over 70o blunt cone with attack angle of 100. (Kn=0.0108)
Figure 23 Normalized density of level 3 refined mesh of a hypersonic flow over 70o blunt cone with attack angle of 100. (Kn=0.0108)
Figure 24 Normalized temperature of level 3 refined mesh of a hypersonic flow over 70o blunt cone with attack angle of 100. (Kn=0.0108)
Figure 25 Streamlines of level 3 refined mesh of a hypersonic flow over 70o blunt cone with attack angle of 100. (Kn=0.0108)
Figure 26 Normalized Mach number of level 3 refined mesh of a hypersonic flow over 70o blunt cone with attack angle of 100. (Kn=0.0108)
(a)
(b)
Figure 27 Surface mesh distribution for a supersonic flow past a sphere (M∞=4.2, Kn∞=0.1035, Argon) (a)with cell quality control (b)without cell quality control
(a)
(b)
Figure 28 Typical distribution surface mesh(1/16 domain) for a single jet case (Kn=0.001, Ps/Pb=150) (a)original mesh (997421 cells) (b)level-1 refined mesh (5522029 cells)
0. preprocessing
I. add node on cell edges II. renumber added nodes III. update connectivity data IV. build neighbor identifier array
Figure 29 Timing for different modules of PAMR at different processors
0
0 2000 4000 6000 8000 10000 12000 14000 16000 18000
2 4 8 16
Processor numbers Time(s)
Figure 30 Total timing for different processors