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AIAA 2002-5531 OBSERVATIONS ON CFD SIMULATION UNCERTAINTIES. Serhat Hosder, Bernard Grossman, William H. Mason, and Layne T. Watson Virginia Polytechnic Institute and State University Blacksburg, VA Raphael T. Haftka University of Florida Gainesville, FL

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aiaa 2002 5531 observations on cfd simulation uncertainties


Serhat Hosder, Bernard Grossman, William H. Mason, and

Layne T. Watson

Virginia Polytechnic Institute and State University

Blacksburg, VA

Raphael T. Haftka

University of Florida

Gainesville, FL

9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization

4-6 September 2002

Atlanta, GA

  • Computational fluid dynamics (CFD) as an aero/hydrodynamic analysis and design tool
  • CFD being used increasingly in multidisciplinary design and optimization (MDO) problems
  • CFD results have an associated uncertainty, originating from different sources
  • Sources and magnitudes of the uncertainty important to assess the accuracy of the results
objective of the paper
Objective of the Paper
  • Finding the magnitude of CFD simulation uncertainties that a well informed user may encounter and analyzing their sources
  • We study 2-D, turbulent, transonic flow in a converging-diverging channel
        • complex fluid dynamics problem
        • affordable for making multiple runs
        • known as “Sajben Transonic Diffuser” in CFD validation studies
transonic diffuser problem
Transonic Diffuser Problem

Weak shock case (Pe/P0i=0.82)




Strong shock case (Pe/P0i=0.72)



Separation bubble

Contour variable: velocity magnitude

uncertainty sources following oberkampf and blottner
Uncertainty Sources (following Oberkampf and Blottner)
  • Physical Modeling Uncertainty
    • PDEs describing the flow
      • Euler, Thin-Layer N-S, Full N-S, etc.
    • boundary conditions and initial conditions
    • geometry representation
    • auxiliary physical models
      • turbulence models, thermodynamic models, etc.
  • Discretization Error
  • Iterative Convergence Error
  • Programming Errors

We show that uncertainties from different sources interact

computational modeling
Computational Modeling
  • General Aerodynamic Simulation Program (GASP)
    • A commercial, Reynolds-averaged, 3-D, finite volume Navier-Stokes (N-S) code
    • Has different solution and modeling options. An informed CFD user still “uncertain” about which one to choose
  • For inviscid fluxes (commonly used options in CFD)
    • Upwind-biased 3rd order accurate Roe-Flux scheme
    • Flux-limiters: Min-Mod and Van Albada
  • Turbulence models (typical for turbulent flows)
    • Spalart-Allmaras (Sp-Al)
    • k- (Wilcox, 1998 version) with Sarkar’s compressibility correction
grids used in the computations
Grids Used in the Computations

Grid 2


A single solution on grid 5 requires approximately 1170 hours of total node CPU time on a SGI Origin2000 with six processors (10000 cycles)

Grid 2 is the typical grid level used in CFD applications

nozzle efficiency
Nozzle efficiency

Nozzle efficiency (neff ), a global indicator of CFD results:

H0i : Total enthalpy at the inlet

He : Enthalpy at the exit

Hes : Exit enthalpy at the state that would be reached by isentropic expansion to the actual pressure at the exit

discretization error by richardson s extrapolation
Discretization Error by Richardson’s Extrapolation

error coefficient

order of the method

a measure of grid spacing

grid level

error in geometry representation1
Error in Geometry Representation

Upstream of the shock, discrepancy between the CFD results of original geometry and the experiment is due to the error in geometry representation.

Downstream of the shock, wall pressure distributions are the same regardless of the geometry used.

downstream boundary condition1
Downstream Boundary Condition

Extending the geometry or changing the exit pressure ratio affect:

  • location and strength of the shock
  • size of the separation bubble
uncertainty comparison in nozzle efficiency
Uncertainty Comparison in Nozzle Efficiency

Strong Shock

Weak Shock

Maximum value of

  • Based on the results obtained from this study,
    • For attached flows without shocks (or with weak shocks), informed users may obtain reasonably accurate results
    • They may get large errors for the cases with strong shocks and substantial separation
  • Grid convergence is not achieved with grid levels that have moderate mesh sizes (especially for separated flows)
  • The flow structure has a significant effect on the grid convergence
  • Difficult to isolate physical modeling uncertainties from numerical errors
  • Uncertainties from different sources interact, especially in the simulation of flows with separation
  • The magnitudes of numerical errors are influenced by the physical models (turbulence models) used
  • Discretization error and turbulence models are dominant sources of uncertainty in nozzle efficiency and they are larger for the strong shock case
  • We should asses the contribution of CFD uncertainties to the MDO problems that include the simulation of complex flows