# Internal zeros for the OFR scheme

**URL:** <https://pyfr.discourse.group/t/internal-zeros-for-the-ofr-scheme/597>\
**Category:** General\
**Created:** [6 May 2022 02:45 UTC](https://pyfr.discourse.group/t/internal-zeros-for-the-ofr-scheme/597 "2022-05-06T02:45:09Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![randommc](https://avatars.discourse-cdn.com/v4/letter/r/e56c9b/32.png) [@randommc](https://pyfr.discourse.group/u/randommc)\
**Post date:** [6 May 2022 02:45 UTC](https://pyfr.discourse.group/t/internal-zeros-for-the-ofr-scheme/597/1 "2022-05-06T02:45:09Z")

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Hi, everyone  
I want to change the correction function to Optimal General FR Schemes (DOI 10.1007/s10915-014-9882-5, Asthana K and Jameson A, High-Order Flux Reconstruction Schemes with Minimal Dispersion and Dissipation),  
 ![image](https://global.discourse-cdn.com/free1/uploads/pyfr/original/1X/34221e4f0418619efed34449ec5933fcbe205045.png). The article only provides the value of internal zeros to P=5. Can anyone tell me the value of internal zeros to P=7?

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**Author:** ![WillT](https://avatars.discourse-cdn.com/v4/letter/w/bc79bd/32.png) [@WillT](https://pyfr.discourse.group/u/WillT)\
**Post date:** [6 May 2022 07:36 UTC](https://pyfr.discourse.group/t/internal-zeros-for-the-ofr-scheme/597/2 "2022-05-06T07:36:29Z")

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In that work the internal zeros were found by optimising the single parameter correction function family of Vincent et al (2010), once they have the c value, it looks as though they then found the zeros of the correction function. In the work by Astana and Jameson they only went up to p=5, so if you wanted to get the internal zeros of this optimised correction function, then you would have to repeat the optimisation for yourself.

Just a point to consider, it is much easier/more accurate to construct the correction function from the c parameter than it is from polynomial zero values. The zeros will have been generated by root finding the exact function defined by c, so you end up with a lot of compounded errors using the zeros.

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**Author:** ![WillT](https://avatars.discourse-cdn.com/v4/letter/w/bc79bd/32.png) [@WillT](https://pyfr.discourse.group/u/WillT)\
**Post date:** [9 May 2022 07:44 UTC](https://pyfr.discourse.group/t/internal-zeros-for-the-ofr-scheme/597/3 "2022-05-09T07:44:10Z")

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A post was split to a new topic: [Compressible Navier–Stokes for incompressible cases](https://pyfr.discourse.group/t/compressible-navier-stokes-for-incompressible-cases/600)