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Higher Order Elements: A Discussion

Higher Order Elements: A Discussion

Aeroacoustic example: Pressure waves from a nozzle. Upper image is treated as linear, lower image is the actual solution.
Also see our blogs on higher-order elements »

CFD code developers are adopting higher-order finite-element CFD methods due to their potential to reduce computation cost while maintaining accuracy. These techniques have been an area of research for many years and are becoming more widely available in popular CFD codes. The webinar will discuss Scott’s research on visualization of higher-order solutions and related development plans for higher-order visualization in Tecplot 360.


  • What are higher-order elements? [0:01:19]
  • Why use higher-order elements? [0:02:29]
  • Post-processing challenges [0:05:23]
  • Tecplot’s research on higher-order element visualization [19:10:22]
  • Tecplot’s 2022 roadmap for higher-order elements [28:52:14]
  • Q&A

The webinar is co-hosted by Dr. Scott Imlay, Tecplot CTO, and Scott Fowler, Tecplot Product Manager.

See Also: Blogs on Higher-Order Elements »

Q&A from the Webinar

The conversation is focused on isosurfaces. How is this different for slices, streamtraces, and particle paths?


A slice is just an isosurface of a coordinate variable, or some linear combination of coordinate variables – if you’re looking at an arbitrary slice. So, the discussion of iso-surfaces applies equally to slices. Since we’re doing sub-division under the hood, the concern is how we render the mesh on slices and isosurfaces. Our intention is to draw the mesh such that it represents the edges of high-order cell rather than the sub-divided cells. Our research code, however, doesn’t do this yet.


Cell sub-division is not a good technique for streamtraces, so we’re researching using the basis functions directly using (r,s,t) coordinates.

Streaklines and Pathlines

Streaklines and pathlines (particle paths) both use interpolation and will be supported. They are very similar to streamtraces in the sense that they are interpolating the solution at a particular point to get the velocity to go to the next point in space. We will eventually allow streaklines and particle paths to utilize the full accuracy of the high-order element, but it’s unlikely to be supported in the first 2022 release. In the first release, Tecplot 360 will assume that the higher-order nodes aren’t there. It’ll still work, it just won’t be as accurate as would be ideal.

Can the geometry and solution have different P-order?

Not with our initial implementation. Our first release assumes that the grid and solution are the same P-order (isoparametric), and we’ll support up to P=3. Our intention is to loosen this restriction in future releases as we understand that a number of CFD codes will use a lower P-order for the geometry and a higher P-order for the solution. If your CFD code has different P-order for the geometry and solution, you’ll have to introduce additional nodes for the geometry to be compatible with our first release.

Do you assume that both the solution and geometrical basis functions are identical?

Yes, we assume they’re identical. If your CFD code does not have identical basis functions for the geometry in the solution, you need to choose one of them, probably the one that is the highest order polynomial. Then you would interpolate the other to that to get to that basis function.

How does Tecplot know what the basis functions are?

You need to tell it. For instance, if you’re reading a CGNS file, it will have the element type in there. It will have, for instance, that this is a Tetra 10, the section of this zone is a Tetra 10 element. That then is stored in the data structures and Tecplot 360 will take advantage of it. In the first release, all basis function will be based on Lagrangian polynomials.

When will support for HOE be implemented in Tecplot 360?

  • Tecplot 360 2021 Release 2 – This release will not have the HOE support we’ve been talking about in this webinar.
  • Tecplot 360 2022 Release 1 – HOE support will be in the 2022 Releases of Tecplot 360. We are putting a stake in the ground, and we’re saying we are going to support higher-order elements, to a certain extent, in our first release of 2022. That will include a lot of what you saw presented today. Higher-order elements will be supported for isosurfaces, slices, and curved meshes.

    CGNS Support – We’re going to be focusing, initially, on compatibility with the CGNS file format. They seem to be about as far along as anybody for higher-order element support within the data files. We’re going to be assuming Lagrangian elements up to P3 and then other features within Tecplot 360 are going to initially ignore the additional nodes.

Which features in Tecplot 360 2022 R1 will treat higher-order elements as linear elements?

Initially, streamtraces, streaklines, particle paths, and derivative calculations will ignore the higher-order nodes. For example, if you want to look at q (vorticity), it’s probably best that you compute it within your CFD code and export that as a variable at this point. We will be adding support for higher-order elements in these areas in the future.

What will be included beyond the initial 2022 release of Tecplot 360?

Beyond the initial release in 2022, we’ll start looking into the streamtrace code using the (r,s,t) technique, and then supporting other file formats. VTK’s VTU file format will be a high priority, and we’ll consider adding a higher-order element support to the Tecplot file formats themselves.

Can I test my HOE code on the Tecplot 360 research?

Yes! Our research code is currently implemented as an add-on (plug-in) to Tecplot 360. The add-on performs the selective sub-division manually to create a new zone composed of the sub-divided cells. Using this add-on, you can understand the underlying technique that Tecplot 360 will eventually have built in.

Partners needed! We encourage you to contact us by emailing Scott Fowler.

If you have an HOE code that you’re using and you want to test any of the research work that we’ve been doing, we want to hear from you. We have a good set of people that we’ve been talking with, but as we get further and further down our development path, we’re going to need more and more people to test this out and give us feedback. 

Is the data from ZJ Wang CGNS format? What version?

Yes, it’s CGNS version 4.

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