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Improvements of the Interpolation
and Non-Orthogonal Correction Schemes in
Caelus
Dr. Chris Sideroff
Dr. Darrin Stephens
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Mesh Quality Issues
• Sensitivity to mesh quality widely reported
• Two main metrics used to quantify “quality”
• Non-orthogonality
• Skewness
• Non-orthogonality tends affect gradient reconstruction, i.e. diffusion
terms
• Skewness tends to affect face interpolation, i.e. convective terms
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Central Interpolation
• Central-based schemes (linear, limitedLinear) are one dimensional –
very susceptible to skewness
d
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Upwind Interpolation
• Include gradient to get better than 1st order accuracy
𝜑𝑓 = 𝜑𝑐 +𝜓( 𝑥𝑓 − 𝑥𝑐)𝜕𝜑
𝜕 𝑥
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Interpolation Schemes Improvements
•linearUpwind
• Does not limit the slope
• Attempts to limit the fluxes
• Introduce commonly used slope limiters that adhere to the TVD
condition
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New Interpolation Schemes
• 8 new interpolation schemes
• Barth-Jespersen: linearUpwindBJ{V}
• Monotonic central: linearUpwindMC{V}
• Differential limiter: linearUpwindDL{V}
• MG: linearUpwindMG{V}
• Minmod: linearUpwindMinmod{V}
• UMIST: linearUpwindUMIST{V}
• VanAlbada: linearUpwindVanAlbada{V}
• VanLeer: linearUpwindVanLeer{V}
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New Interpolation Schemes cont.
• 2 implementations
• Fully implicit
• Deferred correction
• Deferred correction used for more difficult meshes
• Controlled with dictionary:div(phi,U) deferredCorrection Gauss dcLinearUpwindBJV grad(U) 0.5
• 0.5 explicit relaxation factor that multiplies the explicit (high order) part
of the discretization (0 – 1)
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Advecting Step
Tobias Holzmann, http://www.holzmann-cfd.de/index.php/en/numerical-schemes
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Advecting Step
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Advecting Step
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Advecting Step
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Advecting Step
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motorBike Test Case
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Non-orthogonal Correction on Boundaries
• 1st order accuracy near boundaries
• Talks from OFWS 8 and 9
• Personal communication
• Only when grid is non-orthogonal near boundaries
• Almost always
• No correction applied for all patch types except processor and coupled
• OpenFOAM 2.x and foam-extend 3.x
...
forAll(corrVecs.boundaryField(), patchi)
{
fvsPatchVectorField& patchCorrVecs =
corrVecs.boundaryField()[patchi];
if (!patchCorrVecs.coupled())
{
patchCorrVecs = vector::zero;
}
else
{
...
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N.O.C. on Boundaries cont.
• Doesn’t work with wall functions < yet ;-) >
• Wall functions work by modifying vt near wall cell
• Turned on with dictionary setting
•laplacian(DT,T) Gauss linear secondOrderCorrected;
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Fixed Value Boundary Conditions
• Method of manufactured solutions
Caelus 4.10 (OpenFOAM, foam-extend)
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Fixed Value Boundary Conditions
• Method of manufactured solutions
Caelus 5.04
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Fixed Gradient Boundary Conditions
• Method of manufactured solutions
Caelus 4.10 (OpenFOAM, foam-extend)
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Fixed Gradient Boundary Conditions
• Method of manufactured solutions
Caelus 5.04
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corrGauss Gradient Scheme
• Face value unknown – iterate a few times (default = 2)
Caelus 5.04
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What is Caelus?
• Caelus is a fork of OpenFOAM
• Free and open: www.caelus-cml.com
• Supports multiple platforms (Windows, Linux and Mac)
• Robust compilation (Scons: www.scons.org)
• Easy to install
• Verified and validated turbulence models (conforms to most commonly
used variants published in open literature)
• Documentation and validation cases
• Improving algorithmic robustness on non-”perfect” meshes
• Multi-dimensional interpolation
• Improved accuracy on non-”perfect” meshes
• Non-orthogonal boundary correction
• Swak, Python wrapping, etc
• New wall functions, new compressible solvers, more numerical
improvements
4.1
05.0
45.1
0*
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What is Caelus?
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What is Caelus?
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About Applied CCM
• Specialise in the application, support and development of OpenFOAM-
based computational mechanics
• Main developers of Caelus
• People
• Darrin Stephens, Chris Sideroff and Aleks Jemcov*
• Locations
• Australia, Canada and USA
• Engage with customers as their technology partner
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Applied CCM Canada
Dr Chris Sideroff
Phone: 613 276 7472
Email: [email protected]
Web: www.appliedccm.ca
Questions
Applied CCM Pty Ltd
Dr Darrin Stephens
Phone: 03 8376 6962
Email: [email protected]
Web: www.appliedccm.com.au