# Computational Fluid Dynamics 5

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```							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
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
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

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