# Single and double derivative of variables

**URL:** https://discourse.paraview.org/t/single-and-double-derivative-of-variables/16639
**Category:** ParaView Support
**Created:** [May 14, 2025, 11:03pm UTC](https://discourse.paraview.org/t/single-and-double-derivative-of-variables/16639 "2025-05-14T23:03:50Z")
**Posts on this page:** 1
**Showing post:** 19

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### Author: ![Kenichiro-Yoshimi](https://discourse.paraview.org/letter_avatar_proxy/v4/letter/k/ecc23a/32.png) [@Kenichiro-Yoshimi](https://discourse.paraview.org/u/Kenichiro-Yoshimi)
#### Post date: [May 20, 2025, 8:39pm UTC](https://discourse.paraview.org/t/single-and-double-derivative-of-variables/16639/19 "2025-05-20T20:39:48Z")

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Here are some potential checkpoints for this analysis:

- Since ParaView doesn’t have a second derivative function, the **Hessian matrix** is calculated by applying the **first-order accurate gradient (Gradient Filter)** twice.
- Because it’s a first-order accurate gradient, it will be constant within a cell. However, the Gradient Filter maintains continuity by taking the average of the gradient values of the cells sharing a point as the derivative value at that point. Nevertheless, a **loss of accuracy** is likely unavoidable when applying such a derivative twice.
- It’s currently **unclear if the observed artifacts** are a result of applying the first-order accurate gradient twice. We need to check if using a **higher-order accurate derivative from VMTK** improves the situation.

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### Other Concerns:

- Has **cell data been converted to point data**? (It’s advisable to enable this conversion in the Fluent to EnSight format export options.)
- Has the issue of **internal boundaries being outputted** been resolved? (See: [https://discourse.paraview.org/t/fluent-dat-file-export-on-gold-ensight-paraview-format-creating-mesh-lines/16500](https://discourse.paraview.org/t/fluent-dat-file-export-on-gold-ensight-paraview-format-creating-mesh-lines/16500))
- Was the **Gradient Filter applied before cutting the tube**?
- Are there any **ghost cell issues**? (Given that parallel visualization doesn’t appear to be used, this is likely not an issue.)
- Are there **multiple blocks**? If so, applying the **Merge Blocks filter** first might lead to improvements.

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_[View the full topic](https://discourse.paraview.org/t/single-and-double-derivative-of-variables/16639)._