Computational Fluid Dynamics 5

							Computational Fluid Dynamics 5
           Errors
     Professor William J Easson
 School of Engineering and Electronics
     The University of Edinburgh
                Things you can do
1.   Create simple geometries in Star-Design
2.   Produce meshes of different densities and of varying
     density (by changing the parameters before meshing)
3.   Solve for laminar flow in a 2D channel
4.   Present the output in a variety of formats
5.   Solve for 2D laminar jets
6.   Solve for 2D flows with wall attachment
7.   Solve to 1st & 2nd order simulations (check this)
8.   Test the appropriateness of your mesh density (check)
9.   Test the appropriateness of the extent of your domain
                Things you can do
11. Simulate steady, turbulent flow
12. Simulate flow past objects in a domain
13. Calculate the drag coefficient using the sum of forces on
    an object in a flow
14. Determine whether flow solution is dominated by
    hyperbolic, parabolic or elliptic behaviour
15. Utilise time-dependant equations to enhance
    convergence for elliptically-dominated solutions
16. Adapt grids to improve local resolution of flow
17. Simulate time-dependant laminar flow past a cylinder
    (vortex shedding)
           Errors

         Anderson and
Versteek & Malalasekera weak on
            errors
             Main sources of error
• Grid
   – Is it sufficiently fine?
• Physics
   – Are you modelling the physical situation with the
     correct equations?
• Discretisation of Partial Differential Equations
   – Is your solution heavily dependant on the order of the
     solution?
• Numerical errors arising from the limitations of
  your software/hardware
                        Grid
• Test the grid resolution accuracy by refining
  the grid
  – By doubling
  – By gradients in the flow (if doubling not
    possible)
• Plot your solutions and extrapolate to grid
  spacing of zero
  – Richardson extrapolation
                       Extrapolation
• As the grid size is             Final value
  reduced, the values of
  the solution should get
  closer to the value
  obtained under
  conditions of
  minimum grid spacing.
   – Note that the first
     couple of points on the
     right would not give a
     good estimate for the
     final value                           Δx
          Grid over-refinement
• Not possible to over-refine for laminar flow
• In turbulent flow the grid can become too
  fine if it enters the laminar sub-layer
  – Turbulent flow assumes that the law of the wall
    applies – which it does not in the laminar sub-
    layer
  – Solution: check that the y*/y+ values are not
    too small
                     Physics
•   Default in Fluent is laminar solution
•   Is the flow turbulent? (S-A, k-e, RSM)
•   Is the flow compressible?
•   Do you have temperature fluctuations?
•   Is there more than one phase?
•   Is the second phase significant?
    Discretisation of the equations
• Order of solution is that of the first missing term
  in the expansion (discretisation) of the pde
• 1st order can give sufficiently good results in some
  cases
• 2nd order is required for most cases
• If solutions with high degree of accuracy are
  required 4th order can be used
• Solution order and grid refinement can be
  balanced
                Numerical errors
•   Not the problem they once were (16 bit)
•   Arise due to truncation of the numbers
•   Can go to ‘double-precision’ if necessary
•   Watch for unusual limitations
    – Fluent uses real reals – does not scale the
      problem to fit the arithmetic to the processor
    – For very small or very large dimensions the
      onus may be on you to do the scaling
                       Silly Errors
• We are all guilty of these. Even Professors of
  Fluid Dynamics
   – or should that read especially Professors of Fluid
     Dynamics
• A sample:
   –   Solution not actually converged
   –   Modelling the wrong fluid
   –   Not having calculated the Re/Ma/etc before starting
   –   Boundary conditions not set properly (or at all!)
           Verification & Validation
             http://www.grc.nasa.gov/WWW/wind

• Verification
   – The process of determining that a model
     implementation accurately represents the developer’s
     conceptual description of the model and the solution to
     the model
• Validation – solving the right equations
   – The process of determining the degree to which a
     model is an accurate representation of the real world
     from the perspective of the intended use of the model
   – Compare with experimental data
          This week’s exercise
• Create a number of grids in gambit for 2D
  flow past a flat plate perpendicular to the
  flow
• Create a graph of solution values for the
  drag force and hence estimate the ‘real’
  value