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Genias Graphics �Tecplot Europe

Antoine Ligier– M. Sc. Aerospace Engineering

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Summary

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  • What are higher order (HO) elements and why do we use them?
  • Visualization challenges:
    • Iso-surfaces
    • Surfaces

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What are higher order elements

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  • Most FE methods assume linear variation of the solution along elements edges
  • Higher order elements assume a non-linear distribution across the element.
    • Usually a quadratic or higher polynomial
    • Element geometry can be curved
    • Solver has better than 2nd order accuracy

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Why using them?

Better accuracy/cost for vortical flows, aeroacoustics and unsteady simulations.

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“…higher order methods will likely increase in utilization during this timeframe, although currently the ability to visualize results from higher order simulations is highly inadequate.”

CFD Vision 2030, NASA

Visualization challenges

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  • Various dataformats (CGNS, vtu, etc...)

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  • Internal datastructures must be modified

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  • Performant visualization without excess sub-division

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  • Most algorithms currently work for linear elements:
    • Iso-surfaces, slices, contours assume extrema at the nodes
    • Streamlines, streaklines and particle path need to interpolate using HO basis functions
    • Shading of surfaces that may be curved

Visualization challenges

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  • Visualize HO elements using existing linear algorithms
    • HO elements are recursively subdivided into linear elements until the desired accuracy is reached
    • Interpolate to the newly created nodes using the HO basis function
  • Tecplot uses selective sub-division to reduce RAM and CPU costs:
    • Subdivide only cells that contain the isosurface
    • Discard the unneeded sub-elements as the sub division progresses

Iso-surface visualization – basic idea

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Tetrahedra sub-division

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  • Uses only 2.353 sub-tets out of a possible 663.552 sub-elements

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Iso-surface visualization - Prism

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  • Uses only 3.804 sub-tets out of 1.328.104 sub-tets

Iso-surface visualization - Pyramid

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Sub-division

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1.017.000 P2 elements

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Data from Z.J. Wang‘s, hoMusic code

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Iso surface of density

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Uses 1.5Mio sub-tets instead of 113Mio without discarding unneeded elements

Iso-surface visualization - Density

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Surfaces - ONERA M6

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What‘s next?

a.ligier@tecplot.com

l.lippert@tecplot.com

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Implementation in SU2

Edwin van der Weide

Twente university

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Thank you!

Contact me for more information

Antoine Ligier

a.ligier@tecplot.com

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Additional slides

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Basis functions

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Brick/Hex sub-division

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Prism sub-division

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Pyramid sub-division

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Streamtraces

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Tecplot at a glance

  • Founded in 1981 by Boeing engineers – Seattle, WA
  • Largest independent CFD post-processor – 47,000 users worldwide
  • Known for being the most complete and flexible post-processing option
  • Focused on large data and

emerging needs in the

CFD community

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Tecplot 360 EX

  • XY/2D/3D plots and animations in one tool
  • Exports publication-quality plots
  • Stable and easy to use
  • Customizable using Macros and Python scripts
  • User friendly interface

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