Computational Fluid Dynamics 5 Errors

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Computational Fluid Dynamics 5Errors

• Professor William J Easson
• School of Engineering and Electronics
• The University of Edinburgh

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Things you can do

• Create simple geometries in Star-Design
• Produce meshes of different densities and of
  varying density (by changing the parameters
  before meshing)
• Solve for laminar flow in a 2D channel
• Present the output in a variety of formats
• Solve for 2D laminar jets
• Solve for 2D flows with wall attachment
• Solve to 1st 2nd order simulations (check this)
• Test the appropriateness of your mesh density
  (check)
• Test the appropriateness of the extent of your
  domain

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Things you can do

1. Simulate steady, turbulent flow
2. Simulate flow past objects in a domain
3. Calculate the drag coefficient using the sum of
   forces on an object in a flow
4. Determine whether flow solution is dominated by
   hyperbolic, parabolic or elliptic behaviour
5. Utilise time-dependant equations to enhance
   convergence for elliptically-dominated solutions
6. Adapt grids to improve local resolution of flow
7. Simulate time-dependant laminar flow past a
   cylinder (vortex shedding)

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Errors

• Anderson and
• Versteek Malalasekera weak on errors

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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

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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

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Extrapolation
Final value

• As the grid size is 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

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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

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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?

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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

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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

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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!)

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Verification Validationhttp//www.grc.nasa.gov/
WWW/wind

• Verification
• The process of determining that a model
  implementation accurately represents the
  developers 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

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This weeks 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