Trust and Quality in CFD

8/16/2019 Trust and Quality in CFD

1/6

School of Mechanical Aerospace and Civil Engineering

MSc/4th Year Advanced CFD

Trust and Quality in CFD

T. J. Craft

George Begg Building, C41

Reading:J. Ferziger, M. Peric, Computational Methods for Fluid Dynamics H.K. Versteeg, W. Malalasekara, An Introduction to Computa- tional Fluid Dynamics: The Finite Volume Method S.V. Patankar, Numerical Heat Transfer and Fluid Flow No te s: B la ck bo ard a nd CF D/T M we b se rve r:http://cfd.mace.manchester.ac.uk/tmcfd

- People - T. Craft - Online Teaching Material

Trust and Quality in CFD 2011/12 1 / 21

Introduction

◮ A number of CFD modelling and solution methods have been studied.

◮ All involve some level of approximation.

◮ Here we aim to collect together main areas where ‘errors’ arise in CFDsolutions, and how these can be avoided, or their effects minimized.

◮ ‘Error’ in this context is rather general – it mainly refers to differences wemight get between a set of CFD results and ‘real-life’ observations or

measurements.

U Ω

0 100 200 300Theta

-8

-6

-4

-2

0

2

C p

Omega=0

Omega=2

Omega=1

Cp Around Cylinder (k-e, Re=140000)


◮ Trust and Quality issues in CFD become important as it is widely used indesign and analysis, and its quantitative results used in criticalapplications.

◮ It can be relatively easy to get results out of a CFD code, but how do weensure they make sense and can be trusted?

◮ What steps should be taken to check for accuracy and reliability of CFDresults?

◮ In order to answer these, we need to have a good understanding of whereerrors and inaccuracies can arise in the modelling and solution process.


Sources of Errors in CFD

◮ Errors, inaccuracies, and differences between CFD results and laboratoryor real-life measurements arise from a number of sources.

◮ Some errors can, at least in principle, be systematically reduced.

◮ Need to understand how these arise, and check for their influence.

◮ Some mismatches between CFD results and measurements may be dueto mathematical models not fully representing the flow physics.

◮ Need to understand the limits of turbulence and other models.

◮ Other mismatches can arise from incomplete or uncertain problemdefinition.

◮ Need to understand the problem physics, and boundary conditions.

◮ Errors arising from software, or incorrect use of software, can be present.

◮ Need to understand the simulation process well, enabling one tocheck for implementation or usage errors.



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Numerical Errors

◮ These generally refer to differences between the CFD solution and theexact solution of the governing differential equations and boundaryconditions.

◮ Can broadly be put into two categories:

◮ Discretization errors: the discretized equations not representing thedifferential ones exactly.

P E W ∂ U ∂ x

≈ U e −U w ∆x

◮ Convergence errors: the discretized equations not being solvedexactly.

a 11 . . . a 1n

......

a n 1 . . . a nn

φ 1...

φ n

≈

b 1...

b n


Discretization Errors

◮ Analytical derivatives and integrals are approximated in terms of discretenodal variable values.

P E W

∂ U

∂ x ≈

U e −U w ∆x

∂ U

∂ t ≈

U (n +1)−U (n )

∆t

◮ Taylor series expansions can give the order of accuracy of theseapproximations.

◮ Order of accuracy does not tell us the accuracy of one particular solution – it indicates how rapidly errors decrease as the grid spacing (or timestep) is refined.

◮ Note that this convergence rate with grid or time step size will only beobserved for sufficiently small grid spacing or time step.


◮ If we write a Taylor series expansion as

φ e = φ P + ∆x

∂φ

∂ x

P

+ (∆x )2

2!

∂ 2φ

∂ x 2

P

+ · · ·

then the leading order error term is only the largest contribution if ∆x issmall enough that ∆x |∂ 2φ /∂ x 2|


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Convergence Errors

◮ The discretized equations areusually solved in an iterativefashion.

◮ Convergence errors often relate tothis process being stopped whenthe result is still not sufficiently

close to the exact solution of thediscretized equation set.

◮ The difficulty in quantifying this is that we cannot measure the error norm,||φ − φ exact ||, since we do not know φ exact .

◮ Simply performing a fixed number of iterations, or continuing until thesolution changes by only some small amount does not guarantee that theerror will be small.


◮ Best solution is to monitor the residual error:

Res = ||a p φ P −∑a i φ i − s φ ||

◮ Non-dimensionalizing the residual by some physical quantities associatedwith the flow problem definition helps to assess convergence levels.

◮ For example, mass residuals can be normalized by an inlet mass flux,and momentum equation residuals by the inlet momentum flux.

◮ As a rule of thumb, residuals normalized as above should often bebrought down to around 10−4 to give sufficient convergence.

◮ The level of convergence required can be checked by reducing theresiduals further and then comparing the solutions obtained.


Mathematical Modelling Errors

◮ These relate to how well the governing differential equations representthe real flow physics.

◮ For single phase laminar flows the equations can generally be regardedas exact.

◮ Mathematical models are often needed to account for turbulence,chemical reaction and combustion, and other processes,

◮ These models all have some limits of applicability, and some will performbetter or worse than others in particular flow situations.

◮ Choosing the appropriate model(s) for a particular case depends on userexperience, and a knowledge and understanding of the models and flowphysics present in the particular problem.

◮ Model validation, usually by comparison with measured data, in a rangeof flows is therefore vital.


◮ Validation studies, and model performances in many general classes offlows can often be found in the open research literature.

– - – : k -ε ; – – : Basic RSM+GL;- - - : Basic RSM+CL; ——: TCL RSM y

x z



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◮ If applying CFD to a new field, validation studies are needed in order togive confidence in the solutions obtained.

◮ Sensitivity of the solution to models can be tested by simulating the flowusing different schemes (eg. using different turbulence models).

◮ In some cases the choice of model is linked with spatial grid and timestep choices. For example, the use of wall-functions for resolvingnear-wall regions, or the relatively fine grids and small time stepsrequired for models such as LES that resolve some turbulence structures.


Grid Quality

◮ A good quality grid is essential in reducing discretization errors.

◮ Poorly constructed grids can introduce significant discretization errors,and can lead to poor, or very slow, convergence.

◮ High aspect ratio cells should be avoided, particularly when not alignedwith the flow (eg.away from near-wall regions).

◮ Non-uniform grids should beused to give smaller cells incritical flow regions (near walls,around sharp corners, acrossshocks,.. . ).


◮ Sudden changes in grid size introduce interpolationand other errors. Cell growth ratios greater thanaround 1.2 should certainly be avoided.

◮ Poor grid angles also cause interpolation errors, and may requiredeferred correction methods for gradient reconstruction, etc.

◮ Grid cells not aligned with the flow direction tend to lead to numericaldiffusion, so grids should be aligned with the expected flow directionwhere possible.

◮ Some codes allow the use of ‘hanging’ nodes, and other non-matchingcell interfaces. Avoid these if possible – particularly in critical flow regions.


◮ Some grid generators, solvers and post-processing software can report‘measures’ of grid quality, eg. cell aspect ratios, cell skewness, etc.

◮ Grid independence checks should always be performed, so it is best touse grid topologies that can be significantly refined without seriouslydegrading grid quality.

◮ For example, as shown below, grid refinement can lead to high aspectratio cells normal to the flow direction.



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Problem Definition Errors

◮ These generally arise from making assumptions in the problem set-upwhich change the characteristics or behaviour of the flow.

◮ Examples include smoothing out crucial geometrical features, imposingperiodicity or symmetries not present in the real flow, or assuming asteady state when the flow is unsteady.

◮ Flow around a circular cylinder:

U

◮ A Von-Karman vortex street develops in real flows.


◮ Assuming symmetry will prevent theabove pattern from developing.

U

◮ Performing a steady statecalculation will also not give thecorrect pattern (and it may bedifficult to obtain convergence).

◮ Wrong assumptions may be made for inlet or other boundary conditions.

◮ For example, fully developed inlet flowprofiles should not be specified whenthere is only a short entry pipe/duct.


Problem Definition Uncertainties

◮ In some cases flow conditions are not known exactly, and assumptionsmust be made for boundary conditions etc.

◮ Inlet conditions are often not known ingreat detail – a flow rate might be given,but not the detailed velocity distribution.

Q

◮ Detailed turbulence statistics might not have been measured, or reported.

◮ Unfortunately, many fluids problems can be rather sensitive to inputssuch as inlet conditions.

◮ These ‘errors’ cannot be easily removed, but sensitivity tests can beperformed – running a number of simulations with different inletconditions.

◮ This is routinely done in weather prediction, for example, where detailedmeasurements for boundary conditions are not available, yet results canbe highly sensitive to local flow details.


User Errors

◮ Mainly arise from user inexperience or lack of planning.

◮ Incorrect usage of software, or errors in setting flow parameters orboundary conditions may fall into this category.

◮ Incorrect post-processing of results also leads to errors.

◮ These type of errors can usually be avoided by ensuring users know howto run software tools correctly, and understand the flow problem and

process of modelling it.



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Software Errors

◮ Nearly all software has some ‘bugs’ in it.

◮ These can include coding errors, and differences between documentationand actual implementation.

◮ Suitable verification tests can usually identify such problems.

◮ Again, user experience and knowledge of the flow and modelling canhelp to identify where such errors may be present.


Trust and Quality in CFD

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