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

1 01.06.2010 Numerical uncertainties in the computation of the flow in 2D street canyons Jörg Franke Department of Fluid- and Thermodynamics University of Siegen, Germany 13 th Int. Conference on Harmonisation within Atmospheric Dispersion Modelling for Regulatory Purposes – HARMO13 Paris, France, 1-4 June, 2010 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Introduction 2 01.06.2010 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 => only spatial discretisation error Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Example for generalised Richardson extrapolation 3 01.06.2010 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) 1.52 1.52 1.50 1.50 Variable of interest Variable of interest 1.48 1.48 1.46 1.46 1.44 1.44 1.42 1.42 1.40 1.40 1.38 1.38 0 1 2 3 4 5 0 1 2 3 4 5 Grid size Grid size Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Numerical uncertainties for 2D street canyons 4 01.06.2010 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 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Physical and numerical parameters 5 01.06.2010 Computational domain and boundary conditions V ref = 5ms -1 Fixed values from equilibrium profiles Log. law Constant (ABL) with pressure H = 20m equilibrium profiles for k and e Standard rough wall functions (z 0 = 0.05m) • Steady RANS with FLUENT V6.3 • Standard k- e model • Iterative convergence down to machine accuracy Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Grids (W/H = 0.325) 6 01.06.2010 Structured grids with doubling of number of cells Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Analysed variables 7 01.06.2010 Local and integral variables       V HM V x W / 2 , z H Windward wall Leeward wall H H 1 1       P P ( x W , z ) dz P P ( x 0 , z ) dz w l H H 0 0      V P max V x , z 0.125 H Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

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

Results (W/H = 0.325) 9 01.06.2010 Influence of grid resolution Coarse grid 2 Medium grid 1 Fine grid 0 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Results (W/H = 0.600) 10 01.06.2010 Influence of grid resolution Coarse grid 2 Medium grid 1 Fine grid 0 Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Results (W/H = 0.325) 11 01.06.2010 One problem: wall functions for very fine meshes? 0 3 4 1 0  L e e w a r d B o t t o m W i n d w a r d g r i d 0 g r i d 1 1 2 3 g r i d 2 1 0 Fully rough 2 y* 1 0  1 / 4 1 / 2 Transitionally C k y   y * rough  1 1 0 Viscous sublayer 0 1 0 0 0 . 5 1 1 . 5 2 2 . 5 3  Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Results (W/H = 0.600) 12 01.06.2010 One problem: wall functions for very fine meshes? 0 3 4 1 0  L e e w a r d B o t t o m W i n d w a r d g r i d 0 g r i d 1 1 2 3 g r i d 2 1 0 Fully rough 2 y* 1 0  1 / 4 1 / 2 Transitionally C k y   y * rough  1 1 0 Viscous sublayer 0 1 0 0 0 . 5 1 1 . 5 2 2 . 5 3  Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

Results (W/H = 0.325) 13 01.06.2010 Influence of approximation for advective/convective terms k and e 1st, rest All 1st order All 2nd order upwind upwind 2nd order upwind Jörg Franke|Department of Fluid- and Thermodynamics|University of Siegen

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