Numerical uncertainties in the computation of the flow in 2D street - - PowerPoint PPT Presentation

01.06.2010 1 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Numerical uncertainties in the computation

• f the flow in 2D street canyons

Jörg Franke Department of Fluid- and Thermodynamics University of Siegen, Germany

13th Int. Conference on Harmonisation within Atmospheric Dispersion Modelling for Regulatory Purposes – HARMO13 Paris, France, 1-4 June, 2010

01.06.2010 2 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Introduction Aim: Quality assurance and increase of confidence in CFD

• Verification and validation
• Calculation verification = estimation of numerical errors
• Numerical errors due to:
• round-off errors
• incomplete iterative convergence
• discretisation error
• Exact solution not known

=> numerical uncertainty = numerical error x factor of safety

• Here:
• double precision
• iterative convergence down to machine accuracy
• steady RANS solution

=>

• nly spatial discretisation error

01.06.2010 3 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Grid size Variable of interest

1 2 3 4 5 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52

Grid size Variable of interest

1 2 3 4 5 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52

Example for generalised Richardson extrapolation Spatial discretisation uncertainty estimation

• solutions on three sytematically refined grids
• generalised Richardson extrapolation to estimate
• observed order of the (entire) numerical approximations
• extrapolated solution for grid size 0
• multiplication of estimated error with safety factor (here: 1.25)

01.06.2010 4 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Numerical uncertainties for 2D street canyons Aim: spatial discretisation uncertainties for flow variables

• test of the recent editorial policy of the ASME Journal of Fluids

Engineering for the estimation and reporting on numerical uncertainties

• skimming flow regime
• transition regime from 3 to 2 and from 2 to 1 vortices
• aspect ratios so far: W/H = 0.3, 0.325, 0.35, 0.6, 0.625, 0.65

01.06.2010 5 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Physical and numerical parameters Computational domain and boundary conditions

• Steady RANS with FLUENT V6.3
• Standard k-e model
• Iterative convergence down to machine accuracy

Fixed values from equilibrium profiles Standard rough wall functions (z0 = 0.05m) Constant pressure

• Log. law

(ABL) with equilibrium profiles for k and e H = 20m Vref = 5ms-1

01.06.2010 6 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Grids (W/H = 0.325) Structured grids with doubling of number of cells

01.06.2010 7 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Analysed variables Local and integral variables

 

H z , / W x V VHM    2 

 

H z , x V VP 0.125 max   



 

H l

dz ) z , x ( P H P 1



 

H w

dz ) z , W x ( P H P 1

Leeward wall Windward wall

01.06.2010 8 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Uncertainty estimation Depending on solution behavior

R = (medium - fine) / (coarse - medium) I. Monotonic convergence 0 < R < 1 II. Oscillatory convergence

• 1 < R < 0
• III. Monotonic divergence

R > 1

• IV. Oscillatory divergence

R < -1  Only 5 of 24 solutions showed monotonic convergence  No simple uncertainty estimation possible!

01.06.2010 9 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Results (W/H = 0.325) Influence of grid resolution

Coarse grid 2 Medium grid 1 Fine grid 0

01.06.2010 10 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Results (W/H = 0.600) Influence of grid resolution

Coarse grid 2 Medium grid 1 Fine grid 0

01.06.2010 11 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Results (W/H = 0.325) One problem: wall functions for very fine meshes?

 y*

0 . 5 1 1 . 5 2 2 . 5 3 1 0 1 0

1

1 0

2

1 0

3

1 0

4

g r i d g r i d 1 g r i d 2

W i n d w a r d L e e w a r d B

• t t o m

 1 2 3

 



y k C * y

/ / 2 1 4 1



Fully rough Transitionally rough Viscous sublayer

01.06.2010 12 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

 y*

0 . 5 1 1 . 5 2 2 . 5 3 1 0 1 0

1

1 0

2

1 0

3

1 0

4

g r i d g r i d 1 g r i d 2

W i n d w a r d L e e w a r d B

• t t o m

Results (W/H = 0.600) One problem: wall functions for very fine meshes?

 1 2 3

 



y k C * y

/ / 2 1 4 1



Fully rough Transitionally rough Viscous sublayer

01.06.2010 13 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Results (W/H = 0.325) Influence of approximation for advective/convective terms

All 1st order upwind All 2nd order upwind k and e 1st, rest 2nd order upwind

01.06.2010 14 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Summary / Conclusions Numerical uncertainty estimation for 2D street canyons

• skimming flow regime with transition between number of vortices
• only spatial discretisation uncertainty (double precision, iterative

convergence to machine accuracy)

• hardly monotonic convergence for generalised Richardson extrapolation
• flow field is extremely sensitive to
• grid resolution
• approximation of the advective/convective terms
• Standard rough wall functions are problematic with grid refinement