43
1 Preconditioned NS Comp utation with FV Method on Colocated Grid Daniel Lee 東東東東東東東 Dec. 21, 2002

Preconditioned NS Computation with FV Method on Colocated Grid

  • Upload
    xenia

  • View
    62

  • Download
    0

Embed Size (px)

DESCRIPTION

Preconditioned NS Computation with FV Method on Colocated Grid. Daniel Lee 東海大學數學系 Dec. 21, 2002. Outline. Model Equation Test Cases The Discrete Geometry The Discrete Algebraic System Solution Procedure Numerical Results and Discussion. Model Equation. - PowerPoint PPT Presentation

Citation preview

Page 1: Preconditioned NS Computation with FV Method on Colocated Grid

1

Preconditioned NS Computation with FV Method on Colo

cated GridDaniel Lee

東海大學數學系Dec. 21, 2002

Page 2: Preconditioned NS Computation with FV Method on Colocated Grid

2

Outline

Model Equation Test Cases The Discrete Geometry The Discrete Algebraic System Solution Procedure Numerical Results and Discussion

Page 3: Preconditioned NS Computation with FV Method on Colocated Grid

3

Model Equation

x-momentum equation y-momentum equation z-momentum equation continuity equation pressure-poisson equation ( PPE )

Page 4: Preconditioned NS Computation with FV Method on Colocated Grid
Page 5: Preconditioned NS Computation with FV Method on Colocated Grid

5

Test Cases

2D one-side-driven cavity flow two-side-driven cavity flow exact-solution cavity flow3D one-face-driven cavity flow air ventilation

Page 6: Preconditioned NS Computation with FV Method on Colocated Grid
Page 7: Preconditioned NS Computation with FV Method on Colocated Grid

7

Discretization of Geometry

boundary-fitted FV discretization cell-centered FV scheme ghost-cell boundary treatment colocated variables approach

Page 8: Preconditioned NS Computation with FV Method on Colocated Grid
Page 9: Preconditioned NS Computation with FV Method on Colocated Grid

9

Discretization of the PDE central finite differencing for PPE hybrid of UFD and CFD for momentum

eqs with appropriate B.C. treatment, resp

ectively

Page 10: Preconditioned NS Computation with FV Method on Colocated Grid

10

Preconditioned Linear System left-preconditioning with right-preconditioning with Split-preconditioning assume consider ie

bMAxM 11 IAM 1

buAM 1

buM 1

IAM 1

MLUA :bLUxAUL 111 )( bLuAUL 111

Uxu

Page 11: Preconditioned NS Computation with FV Method on Colocated Grid

11

基本測試

Page 12: Preconditioned NS Computation with FV Method on Colocated Grid

12

Possion 方程: ,運用 CG 迭代方法

preconditioner

nx, ny iter res r_res max err cpu ratio

None-CG 160 548 8.11e-05 9.30e-11 1.21e-09 9.907 1.000

Jacobi-CG 160 548 8.11e-05 9.30e-11 1.21e-09 9.178 0.926

SGS-CG 160 195 7.12e-05 8.16e-11 1.12e-09 5.914 0.596

SSOR-CG 160 58 6.57e-05 7.54e-11 5.61e-10 1.831 0.184

ILU(0)-CG 160 164 7.50e-05 8.60e-11 1.05e-09 4.564 0.460

MILU(0)-CG

160 57 6.17e-05 7.08e-11 1.64e-10 1.640 0.165

33 yxU

Page 13: Preconditioned NS Computation with FV Method on Colocated Grid

13

Possion 方程:,運用 CG 迭代方法

preconditioner

nx, ny iter res r_res max err cpu ratio

None-CG

160 546 2.28e-04 9.51e-11 1.43e-06 9.028 1.000

Jacobi-CG

160 546 2.28e-04 9.51e-11 1.43e-06 9.216 1.020

SGS-CG

160 194 2.19e-04 9.14e-11 1.42e-06 5.892 0.652

SSOR-CG

160 58 1.72e-04 7.19e-11 1.43e-06 1.837 0.203

ILU(0)-CG

160 163 2.36e-04 9.86e-11 1.42e-06 4.468 0.494

MILU(0)-CG

160 18 2.07e-04 8.64e-11 1.43e-06 0.571 0.062

yxeU

Page 14: Preconditioned NS Computation with FV Method on Colocated Grid

14

Possion 方程:,運用 BiCG 迭代方法

preconditioner

nx, ny iter res r_res max err cpu ratio

None-BiCG

160 548 8.11e-05 9.30e-11 1.21e-09 16.661 1.000

Jacobi-BiCG

160 548 8.11e-05 9.30e-11 1.21e-09 18.076 1.082

SGS-BiCG 160 195 7.12e-05 8.16e-11 1.12e-09 10.725 0643

SSOR-BiCG

160 58 6.57e-05 7.54e-11 5.61e-10 3.050 0.183

ILU(0)- BiCG

160 164 7.50e-05 8.60e-11 1.05e-09 7.713 0.462

MILU(0)- BiCG

160 57 8.12e-05 9.31e-11 8.41e-10 2.767 0.166

33 yxU

Page 15: Preconditioned NS Computation with FV Method on Colocated Grid

15

Possion 方程:,運用 BiCG 迭代方法 precondit

ionernx, ny iter iter r_res r_res r_res r_res

None-BiCG

160 Res Res max err max err max err max err

Jacobi-BiCG

160 546 546 cpu cpu cpu cpu

SGS-BiCG 160 2.28e-04 2.28e-04 ratio ratio ratio ratio

SSOR-BiCG

160 546 546 9.51e-11 9.51e-11 9.51e-11 9.51e-11

ILU(0)- BiCG

160 2.28e-04 2.28e-04 1.43e-06 1.43e-06 1.43e-06 1.43e-06

MILU(0)- BiCG

160 194 194 17.096 17.096 17.096 17.096

yxeU

Page 16: Preconditioned NS Computation with FV Method on Colocated Grid

16

Possion 方程:,運用 CGS 迭代方法 precondition

ernx, ny iter res r_res max err cpu ratio

None-CGS 160 428 8.58e-05 9.84e-11 1.52e-11 13.109 1.000

Jacobi-CGS 160 428 8.58e-05 9.84e-11 1.52e-11 13.847 1.051

SGS-CGS 160 130 7.88e-05 9.04e-11 9.88e-09 6.993 0.533

SSOR-CGS 160 36 8.70e-05 9.98e-11 7.66e-09 1.959 0.149

ILU(0)- CGS 160 121 7.65e-05 8.78e-11 7.82e-11 5.866 0.447

MILU(0)- CGS

160 77 3.65e-05 4.19e-11 7.92e-11 3.859 0.294

33 yxU

Page 17: Preconditioned NS Computation with FV Method on Colocated Grid

17

Possion 方程:,運用 CGS 迭代方法

preconditioner

nx, ny iter Res r_res max err

cpu ratio

None-CGS

160 428 2.31e-04

9.63e-11

1.43e-06

13.090 1.000

Jacobi-CGS

160 428 2.31e-04

9.63e-11

1.43e-06

14.182 1.083

SGS-CGS

160 130 1.91e-04

7.99e-11

1.43e-06

6.902 0.521

SSOR-CGS

160 38 4.18e-04

1.75e-11

1.42e-06

2.168 0.165

ILU(0)- CGS

160 121 1.78e-04

7.43e-11

1.42e-06

5.799 0.442

MILU(0)- CGS

160 23 1.34e-04

5.61e-11

1.43e-06

1.203 0.091

yxeU

Page 18: Preconditioned NS Computation with FV Method on Colocated Grid

18

Possion 方程:,運用 BiCGs 迭代方法

preconditioner

nx, ny iter res r_res max err cpu ratio

None-BiCGs

160 389 7.98e-05 9.15e-11 1.47e-08 12.826 1.000

Jacobi-BiCGs

160 382 8.65e-05 9.92e-11 3.23e-08 12.630 0.984

GS-BiCGs 160 488 5.31e-05 6.09e-11 4.77e-09 20.532 1.600

SGS-BiCGs 160 141 7.99e-05 9.17e-11 2.37e-08 7.458 0.581

SOR-BiCGs 160 294 8.14e-05 9.33e-11 1.33e-08 12.532 0.980

SSOR-BiCGs

160 35 1.73e-05 1.98e-11 2.06e-09 1.900 0.148

ILU(0)- BiCGs

160 119 8.48e-05 9.73e-11 2.15e-08 5.834 0.454

MILU(0)- BiCGs

160 37 6.48e-05 7.43e-11 4.75e-10 1.861 0.145

33 yxU

Page 19: Preconditioned NS Computation with FV Method on Colocated Grid

19

Possion 方程:,運用 BiCGs 迭代方法

yxeU

preconditioner

nx, ny iter res r_res max err cpu ratio

None-BiCGs 160 381 2.07e-04 8.64e-11 1.42e-06 12.195 1.000

Jacobi-BiCGs 160 387 2.34e-04 9.75e-11 1.41e-06 13.047 1.069

GS-BiCGs 160 407 3.06e-05 1.28e-11 1.43e-06 17.238 1.413

SGS-BiCGs 160 136 1.98e-04 8.28e-11 1.38e-06 7.177 0.580

SOR-BiCGs 160 350 1.42e-04 5.91e-11 1.49e-06 14.737 1.208

SSOR-BiCGs 160 34 9.56e-05 3.99e-11 1.43e-06 1.833 0.150

ILU(0)- BiCGs 160 115 2.05e-04 8.57e-11 1.39e-06 5.667 0.464

MILU(0)- BiCGs

160 13 1.81e-04 7.55e-11 1.43e-06 0.688 0.055

Page 20: Preconditioned NS Computation with FV Method on Colocated Grid

20

Possion 方程: ,運用

GMRES(80) 迭代方法測試不同 restart 值的結果 33 yxU

preconditioner

nx, ny iter res r_res max err cpu

GMRES 80 275 1.36e-05 8.72e-11 1.42e-06 10.986

GMRES(10)

80 2426 1.56e-05 9.95e-11 1.41e-06 12.932

GMRES(20)

80 1313 1.56e-05 9.98e-11 1.43e-06 8.472

GMRES(30)

80 968 1.55e-05 9.90e-11 1.38e-06 7.418

GMRES(50)

80 698 1.56e-05 9.98e-11 1.49e-06 6.993

GMRES(80)

80 470 1.49e-05 9.56e-11 1.43e-06 6.412

GMRES(100)

80 444 1.51e-05 9.67e-11 1.39e-06 7.073

Page 21: Preconditioned NS Computation with FV Method on Colocated Grid

21

Possion 方程:,運用 GMRES(80) 迭代方法

33 yxU

preconditioner nx, ny iter res r_res max err cpu ratio

None-GMRES 80 470 1.49e-05 9.56e-11 8.36e-09 6.412 1.000

Jacobi-GMRES 80 470 5.84e-05 9.56e-11 8.36e-09 6.501 1.013

GS-GMRES 80 415 7.73e-05 9.53e-11 5.76e-09 6.077 0.947

SGS-GMRES 80 107 9.82e-05 8.57e-11 1.95e-09 1.557 0.242

SOR-GMRES 80 333 2.31e-04 9.97e-11 1.90e-09 4.877 0.760

SSOR-GMRES 80 41 7.98e-05 6.61e-11 6.88e-10 0.478 0.074

ILU(0)- GMRES 80 85 1.46e-04 9.41e-11 6.11e-10 1.309 0.204

MILU(0)- GMRES 80 38 6.33e-04 9.23e-11 4.96e-10 0.415 0.064

Page 22: Preconditioned NS Computation with FV Method on Colocated Grid

22

Possion 方程:,運用 GMRES(80) 迭代方法

yxeU

preconditioner

nx, ny iter res r_res max err cpu ratio

None-GMRES

80 580 4.26e-05 9.95e-11 5.73e-06 7.945 1.000

Jacobi-GMRES

80 580 1.66e-05 9.95e-11 5.73e-06 7.983 1.004

GS-GMRES 80 437 2.21e-05 9.89e-11 5.76e-06 6.320 0.795

SGS-GMRES 80 106 2.92e-05 9.20e-11 5.77e-06 1.531 0.192

SOR-GMRES 80 325 7.29e-05 9.99e-11 5.77e-06 4.867 0.612

SSOR-GMRES

80 40 4.60e-05 8.83e-11 5.77e-06 0.462 0.058

ILU(0)- GMRES

80 85 3.54e-05 8.29e-11 5.77e-06 1.367 0.172

MILU(0)- GMRES

80 17 2.47e-04 9.66e-11 5.78e-06 0.165 0.020

Page 23: Preconditioned NS Computation with FV Method on Colocated Grid

23

Possion 方程:,運用 QMR 迭代方法

33 yxU

preconditioner

nx, ny iter res r_res max err cpu ratio

None-QMR

160 532 8.40e-05 9.63e-11 5.30e-09 21.260 1.000

Jacobi-QMR

160 532 8.40e-05 9.63e-11 5.30e-09 22.076 1.038

SGS-QMR

160 189 8.41e-05 9.65e-11 5.07e-09 11.600 0.545

SSOR-QMR

160 57 6.38e-05 7.32e-11 1.35e-09 3.816 0.179

ILU(0)- QMR

160 159 8.69e-05 9.96e-11 5.05e-09 8.982 0.422

MILU(0)- QMR

160 59 3.79e-05 4.35e-11 1.10e-10 3.518 0.165

Page 24: Preconditioned NS Computation with FV Method on Colocated Grid

24

Possion 方程:,運用 QMR 迭代方法

yxeU

preconditioner

nx, ny iter Res r_res max err

cpu Ratio

None-QMR

160 529 2.36e-04

9.86e-11

1.41e-06

21.173 1.000

Jacobi-QMR

160 529 2.36e-04

9.86e-11

1.41e-06

21.673 1.023

SGS-QMR

160 188 2.37e-04

9.88e-11

1.41e-06

11.581 0.546

SSOR-QMR

160 57 1.63e-04

6.79e-11

1.43e-06

3.619 0.170

ILU(0)- QMR

160 159 2.08e-04

8.67e-11

1.41e-06

9.088 0.429

MILU(0)- QMR

160 19 1.75e-04

7.29e-11

1.43e-06

1.262 0.050

Page 25: Preconditioned NS Computation with FV Method on Colocated Grid

25

Possion 方程: ,運用 BiCGs

迭代方法搭配預優化算子 SOR 測試不同 w 的結果 yxeU

preconditioner nx, ny iter res r_res max err cpu ratio

SOR-BiCGs(w=1.0) 160 407 3.06e-05 1.28e-11 1.43e-06 17.434 1.000

SOR-BiCGs(w=1.1) 160 390 1.59e-04 6.64e-11 6.64e-06 16.192 0.928

SOR-BiCGs(w=1.2) 160 421 1.83e-04 7.62e-11 7.62e-06 17.428 0.999

SOR-BiCGs(w=1.3) 160 489 2.16e-04 9.03e-11 9.03e-06 20.788 1.192

SOR-BiCGs(w=1.4) 160 378 9.59e-05 4.00e-11 4.00e-06 15.785 0.905

SOR-BiCGs(w=1.5) 160 421 2.20e-04 9.20e-11 9.20e-06 17.557 1.007

SOR-BiCGs(w=1.6) 160 389 6.84e-05 2.86e-11 2.86e-06 16.376 0.939

SOR-BiCGs(w=1.7) 160 343 1.92e-04 8.02e-11 8.02e-06 14.387 0.825

SOR-BiCGs(w=1.8) 160 347 2.32e-04 9.66e-11 9.66e-06 14.548 0.834

SOR-BiCGs(w=1.9) 160 350 1.42e-04 5.91e-11 5.91e-06 14.699 0.843

Page 26: Preconditioned NS Computation with FV Method on Colocated Grid

26

Possion 方程: ,運用 BiCGs

迭代方法搭配預優化算子 SSOR 測試不同 w 的結果 yxeU

preconditioner nx, ny iter res r_res max err cpu ratio

SSOR-BiCGs(w=1.0)

160 136 1.98e-04 8.28e-11 1.38e-06 7.200 1.000

SSOR-BiCGs(w=1.1)

160 125 2.02e-04 8.41e-11 1.36e-06 6.652 0.923

SSOR-BiCGs(w=1.2)

160 113 2.28e-04 9.53e-11 1.35e-06 5.991 0.832

SSOR-BiCGs(w=1.3)

160 102 1.43e-04 5.98e-11 1.48e-06 5.362 0.744

SSOR-BiCGs(w=1.4)

160 92 1.82e-04 7.61e-11 1.32e-06 4.968 0.690

SSOR-BiCGs(w=1.5)

160 84 8.86e-05 3.70e-11 1.38e-06 4.439 0.616

SSOR-BiCGs(w=1.6)

160 66 2.03e-04 8.47e-11 1.37e-06 3.605 0.500

SSOR-BiCGs(w=1.7)

160 56 1.30e-04 5.43e-11 1.49e-06 2.983 0.414

SSOR-BiCGs(w=1.8)

160 48 1.86e-04 7.78e-11 1.43e-06 2.594 0.360

SSOR-BiCGs(w=1.9)

160 34 9.56e-05 3.99e-11 1.43e-06 1.833 0.254

Page 27: Preconditioned NS Computation with FV Method on Colocated Grid

27

Possion 方程: ,運用

GMRES(80) 迭代方法測試左預優化和右預優化 yxeU

preconditioner nx, ny iter res r_res max err cpu

Jacobi-GMRES(L) 160 1546 2.32e-04 9.91e-11 1.31e-06 169.143

Jacobi-GMRES(R) 160 1546 2.37e-04 9.91e-11 1.31e-06 170.852

SGS- GMRES(L) 160 311 4.03e-04 9.03e-11 1.42e-06 36.671

SGS- GMRES(R) 160 304 2.09e-04 8.72e-11 1.40e-06 35.380

SSOR- GMRES(L) 160 57 6.39e-04 8.37e-11 1.43e-06 5.500

SSOR- GMRES(R) 160 55 2.21e-04 9.21e-11 1.42e-06 5.200

ILU(0)- GMRES(L) 160 247 5.86e-04 9.76e-11 1.42e-06 28.311

ILU(0)- GMRES(R) 160 238 2.34e-04 9.77e-11 1.42e-06 28.054

MILU(0)- GMRES(L)

160 21 4.75e-04 9.30e-11 1.43e-06 1.284

MILU(0)- GMRES(R)

160 18 1.74e-04 7.24e-11 1.44e-06 1.093

Page 28: Preconditioned NS Computation with FV Method on Colocated Grid

28

Possion 方程: ,運用

QMR(80) 迭代方法測試左預優化和右預優化 yxeU

preconditioner nx, ny iter res r_res max err cpu

Jacobi-QMR(L) 160 529 2.36e-04 9.86e-11 1.41e-06 21.712

Jacobi-QMR(R) 160 529 2.36e-04 9.86e-11 1.41e-06 22.068

SGS- QMR(L) 160 188 2.37e-04 9.88e-11 1.41e-06 11.696

SGS- QMR(R) 160 188 2.38e-04 9.95e-11 1.41e-06 11.678

SSOR- QMR(L) 160 57 1.63e-04 6.79e-11 1.43e-06 3.676

SSOR- QMR(R) 160 57 1.73e-04 7.24e-11 1.43e-06 3.653

ILU(0)- QMR(L) 160 159 2.08e-04 8.67e-11 1.41e-06 9.041

ILU(0)- QMR(R) 160 159 2.08e-04 8.67e-11 1.41e-06 9.099

MILU(0)- QMR(L) 160 19 1.75e-04 7.29e-11 1.43e-06 1.148

MILU(0)- QMR(R) 160 19 1.81e-04 7.57e-11 1.43e-06 1.198

Page 29: Preconditioned NS Computation with FV Method on Colocated Grid

29

應用測試2D

Page 30: Preconditioned NS Computation with FV Method on Colocated Grid

30

單邊驅動穴流:運用 CG 迭代方法測試 , nx=ny=80 preconditioner

t_steps iter cpu_total

final_res

diff_u Diff_v Diff_p ratio

None-CG

52 12513 33.88 1.2e-05 4.4e-03 2.6e-03 3.3e-03 1.000

Jacobi-CG

52 12394 33.73 1.1e-05 4.4e-03 2.6e-03 3.3e-03 0.995

SGS- CG

52 4931 24.46 3.4e-06 4.4e-03 2.6e-03 3.3e-03 0.721

SSOR- CG

52 2984 14.52 3.3e-06 4.4e-03 2.6e-03 3.3e-03 0.428

ILU(0)- CG

52 4354 20.85 2.8e-06 4.4e-03 2.6e-03 3.3e-03 0.615

MILU(0)-CG

52 3073 15.25 1.0e-07 4.4e-03 2.6e-03 3.3e-03 0.450

Page 31: Preconditioned NS Computation with FV Method on Colocated Grid

31

單邊驅動穴流:運用 BiCG 迭代方法測試 ,nx=ny=80 preconditioner

t_steps iter cpu_total

final_res

diff_u Diff_v Diff_p ratio

None-BiCG

52 12513 67.80 1.2e-05 4.4e-03 2.6e-03 3.3e-03 1.000

Jacobi-BiCG

52 12394 67.40 1.1e-05 4.4e-03 2.6e-03 3.3e-03 0.994

SGS- BiCG

52 4931 44.88 3.4e-06 4.4e-03 2.6e-03 3.3e-03 0.661

SSOR- BiCG

52 2984 27.86 3.3e-06 4.4e-03 2.6e-03 3.3e-03 0.410

ILU(0)- BiCG

52 4354 37.88 2.8e-06 4.4e-03 2.6e-03 3.3e-03 0.558

MILU(0)-BiCG

52 3073 26.93 1.0e-07 4.4e-03 2.6e-03 3.3e-03 0.397

Page 32: Preconditioned NS Computation with FV Method on Colocated Grid

32

單邊驅動穴流:運用 CGS 迭代方法測試 , nx=ny=80 preconditioner

t_steps iter cpu_total

final_res

diff_u Diff_v Diff_p ratio

None-CGS

52 9305 48.22 4.8e-04 4.4e-03 2.6e-03 3.3e-03 1.000

Jacobi-CGS

52 9284 48.28 1.1e-04 4.4e-03 2.6e-03 3.3e-03 1.001

SGS- CGS

52 3440 29.48 6.5e-07 4.4e-03 2.6e-03 3.3e-03 0.611

SSOR- CGS

52 2305 19.62 1.9e-06 4.4e-03 2.6e-03 3.3e-03 0.406

ILU(0)- CGS

52 2973 25.81 2.3e-06 4.4e-03 2.6e-03 3.3e-03 0.535

MILU(0)-CGS

52 2377 20.88 1.3e-07 4.4e-03 2.6e-03 3.3e-03 0.433

Page 33: Preconditioned NS Computation with FV Method on Colocated Grid

33

單邊驅動穴流:運用 BiCGs 迭代方法測試 , nx=ny=80 preconditio

nert_steps iter cpu_total final_res diff_u Diff_v Diff_p ratio

None-BiCGs 52 8686 46.79 5.6e-06 4.4e-03 2.6e-03 3.3e-03 1.000

Jacobi-BiCGs

52 8548 46.42 4.3e-06 4.4e-03 2.6e-03 3.3e-03 0.992

GS- BiCGs 52 7210 54.36 3.6e-05 4.4e-03 2.6e-03 3.3e-03 1.161

SGS- BiCGs 52 3521 29.72 1.9e-05 4.4e-03 2.6e-03 3.3e-03 0.635

SOR- BiCGs 52 7022 52.14 4.3e-07 4.4e-03 2.6e-03 3.3e-03 1.111

SSOR- BiCGs

52 2497 21.39 3.5e-07 4.4e-03 2.6e-03 3.3e-03 0.457

ILU(0)- BiCGs

52 3074 27.82 3.6e-06 4.4e-03 2.6e-03 3.3e-03 0.594

MILU(0)-BiCGs

52 2120 19.46 1.1e-07 4.4e-03 2.6e-03 3.3e-03 0.415

Page 34: Preconditioned NS Computation with FV Method on Colocated Grid

34

單邊驅動穴流:運用 GMRES(80) 迭代方法測試 ,nx=ny=80

preconditioner

t_steps iter cpu_total final_res diff_u Diff_v Diff_p ratio

Jacobi-GMRES

52 23187 298.21 6.3e-07 4.4e-03 2.6e-03 3.3e-03 1.000

SGS- GMRES

52 5428 73.29 4.4e-07 4.4e-03 2.6e-03 3.3e-03 0.245

SSOR- GMRES

52 3207 42.45 4.7e-06 4.4e-03 2.6e-03 3.3e-03 0.142

ILU(0)- GMRES

52 4793 67.73 8.4e-07 4.4e-03 2.6e-03 3.3e-03 0.227

MILU(0)-GMRES

52 2391 27.58 1.1e-07 4.4e-03 2.6e-03 3.3e-03 0.092

Page 35: Preconditioned NS Computation with FV Method on Colocated Grid

35

單邊驅動穴流:運用 QMR 迭代方法測試 , nx=ny=80 preconditio

nerT_steps iter cpu_total final_res diff_u Diff_v Diff_p ratio

None-QMR 52 14030 95.37 1.3e-07 4.4e-03 2.6e-03 3.3e-03 1.000

Jacobi-QMR

52 13870 95.20 1.3e-07 4.4e-03 2.6e-03 3.3e-03 0.998

SGS- QMR 52 5107 53.35 1.2e-07 4.4e-03 2.6e-03 3.3e-03 0.559

SSOR- QMR

52 3245 34.64 1.1e-07 4.4e-03 2.6e-03 3.3e-03 0.363

ILU(0)- QMR

52 4751 48.50 1.2e-07 4.4e-03 2.6e-03 3.3e-03 0.508

MILU(0)-QMR

52 3403 35.03 1.0e-07 4.4e-03 2.6e-03 3.3e-03 0.367

Page 36: Preconditioned NS Computation with FV Method on Colocated Grid

36

單邊驅動穴流:運用 CG 迭代方法測試 , nx=ny=160 preconditio

nerT_steps iter cpu_total final_res diff_u Diff_v Diff_p ratio

none-CG 205 89946 1311.69 2.9e-05 1.1e-03 6.6e-04 8.3e-04 1.000

Jacobi-CG 205 89735 1354.58 2.8e-05 1.1e-03 6.6e-04 8.3e-04 1.032

SGS- CG 205 33976 864.04 8.0e-06 1.1e-03 6.6e-04 8.3e-04 0.658

SSOR- CG 205 16240 417.24 5.2e-06 1.1e-03 6.6e-04 8.3e-04 0.318

ILU(0)- CG 205 29054 659.31 6.3e-06 1.1e-03 6.6e-04 8.3e-04 0.502

MILU(0)-CG

205 20511 480.99 4.2e-08 1.1e-03 6.6e-04 8.3e-04 0.365

Page 37: Preconditioned NS Computation with FV Method on Colocated Grid

37

單邊驅動穴流:運用 BiCGs 迭代方法測試 , nx=ny=160 precondit

ionerT_steps iter cpu_total final_res diff_u Diff_v Diff_p ratio

none-BiCGs

205 49880 1354.25 1.7e-04 1.1e-03 6.6e-04 8.3e-04 1.000

Jacobi-BiCGs

205 49760 1384.64 2.8e-04 1.1e-03 6.6e-04 8.3e-04 1.009

SGS- BiCGs

205 24046 1129.74 6.6e-06 1.1e-03 6.6e-04 8.3e-04 0.565

SSOR- BiCGs

205 10857 503.66 2.8e-06 1.1e-03 6.6e-04 8.3e-04 0.277

ILU(0)- BiCGs

205 20640 864.64 2.1e-05 1.1e-03 6.6e-04 8.3e-04 0.446

MILU(0)-BiCGs

205 13635 580.72 2.5e-08 1.1e-03 6.6e-04 8.3e-04 0.311

Page 38: Preconditioned NS Computation with FV Method on Colocated Grid

38

單邊驅動穴流:運用 QMR 迭代方法測試 , nx=ny=160 preconditio

nerT_steps iter cpu_total final_res diff_u Diff_v Diff_p ratio

none-QMR 205 109019 3778.75 4.2e-08 1.1e-03 6.6e-04 8.3e-04 1.000

Jacobi-QMR

205 108363 3814.11 4.3e-08 1.1e-03 6.6e-04 8.3e-04 1.022

SGS- QMR 205 38589 2136.44 4.0e-08 1.1e-03 6.6e-04 8.3e-04 0.834

SSOR- QMR

205 18865 1047.75 4.2e-08 1.1e-03 6.6e-04 8.3e-04 0.371

ILU(0)- QMR

205 32659 1685.48 4.2e-08 1.1e-03 6.6e-04 8.3e-04 0.638

MILU(0)-QMR

205 22603 1177.33 4.3e-08 1.1e-03 6.6e-04 8.3e-04 0.428

Page 39: Preconditioned NS Computation with FV Method on Colocated Grid
Page 40: Preconditioned NS Computation with FV Method on Colocated Grid
Page 41: Preconditioned NS Computation with FV Method on Colocated Grid
Page 42: Preconditioned NS Computation with FV Method on Colocated Grid
Page 43: Preconditioned NS Computation with FV Method on Colocated Grid

43

應用測試3D