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Robust Mesh Deformation in SU2 Using Radial Basis Function Interpolation

Floyd van Steen, Matteo Pini, Carlo de Servi, Piero Colonna

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Background

  • Why robust mesh deformation?
    • Preventing negative effect of low mesh quality on convergence
    • Maintaining largest possible design space

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Background

  • Why robust mesh deformation?
    • Preventing negative effect of low mesh quality on convergence
    • Maintaining largest possible design space
  • Challenges mesh deformation:
    • Small wall clearances
    • Periodic domains
    • Inflation layer

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Background

  • Why robust mesh deformation?
    • Preventing negative effect of low mesh quality on convergence
    • Maintaining largest possible design space
  • Challenges mesh deformation:
    • Small wall clearances
    • Periodic domains
    • Inflation layer

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Background

  • Why robust mesh deformation?
    • Preventing negative effect of low mesh quality on convergence
    • Maintaining largest possible design space
  • Challenges mesh deformation:
    • Small wall clearances
    • Periodic domains
    • Inflation layer
  • RBF interpolation
    • Robust
    • Efficient
    • Modifiable

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Methodology

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Radial Basis Function Interpolation

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Sliding Boundary Node Algorithm

  • Aims at preserving orthogonality during deformation
  • Sliding along boundary by a free displacement and normal projection to surface

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Initial mesh

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Sliding Boundary Node Algorithm

  • Aims at preserving orthogonality during deformation
  • Sliding along boundary by a free displacement and normal projection to surface

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Initial mesh

Free displacement

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Sliding Boundary Node Algorithm

  • Aims at preserving orthogonality during deformation
  • Sliding along boundary by a free displacement and normal projection to surface

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Initial mesh

Free displacement

Normal projection

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Periodicity

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Inflation Layer Preservation

  • Free displacement and projection to inflation layer height

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Initial mesh

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Inflation Layer Preservation

  • Free displacement and projection to inflation layer height

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Initial mesh

Displaced inflation layer edge

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Inflation Layer Preservation

  • Free displacement and projection to inflation layer height

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Initial mesh

Displaced inflation layer edge

Projected inflation layer edge

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Inflation Layer Preservation

  • Free displacement and projection to inflation layer height

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Initial mesh

Displaced inflation layer edge

Projected inflation layer edge

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Data Reduction Methods

  • Increased computational efficiency by using a reduced set of control nodes
  • Double-edged greedy algorithm
  • Iteratively adding control nodes based on maximum error and error direction
  • Tolerance based on % of maximum surface deformation

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Results

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Test Case

  • 3D Fluid domain (0.13 x 0.2 x 0.2) with 4 solid pins
  • Pins subjected to equal deformation
  • Deformation settings:
    • RBF support radius: 0.005
    • Data reduction tolerance: 1% of max deformation

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Undeformed pin

Deformed pin

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Results

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Spanwise min. orthogonality

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Results

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Spanwise min. orthogonality

ELA

RBF

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Inflation Layer Preservation

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RBF

RBF with ILP

ELA

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Solid Pin Deformation

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Outlook

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Outlook

  • Further development of RBF mesh deformation (PR #2240)
  • Implementation into discrete adjoint optimisation design chain

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Thank you!

Floyd van Steen

PhD Candidate

Propulsion & Power Group

TU Delft, the Netherlands

Email: F.A.vanSteen@tudelft.nl