[Other] Effcient WENO Scheme

janGaertner · October 21, 2020, 15:41

Hello all,

in the recent months I had put a lot of work into the WENO Scheme originally written by Tobias Martin to improve efficiency and computational speed.
It has finally reached a state that is stable and has proven to reach the accuracy and performance that I would expect from this scheme. This has been now also published in SoftwareX describing some of the improvements and the test cases (https://doi.org/10.1016/j.softx.2020.100611).

If you are looking for a higher order scheme which also works for discontinuities in flows, such as shocks, this would be a good choice. Please check it out on GitHub
https://github.com/WENO-OF/WENOEXT

Hope some of you will find it helpful

(If you find any bugs or have ideas how to improve it please send me an e-mail or open an issue)

janGaertner · November 5, 2020, 07:17

Hello,

I am sorry to say that there was a major bug in the latest release of the library. In the release 2.0 the integer power multiplication for the Gauss quadratur was incorrect for any order higher than 2. Sadly this mistake did not appear in any of my small test cases. However, the release 1.0 which is used for the publication is correct.

I have now fixed this error and released 2.1 version which should fix this issue.

li siye · December 7, 2020, 09:11

Thank you for your amazing jobs! Jan Gaertner!

I have a big problem that if i use dynamicRefineFvMesh (AMR method), how can i also use the WENO library to get the stencil where the level and size of cells are different, how can deal with this problem.

Thanks a lot again! Best wishes to you!

janGaertner · December 8, 2020, 04:33

Hello Siye,

the calculation of the stencil list and corresponding matrices is computationally very expensive. Therefore, it is currently implemented to be done only once when the scheme is called the first time, after this the matrix and stencil lists are stored as a static object. Thus, you cannot recreate this list at run time, which conflicts with adaptive mesh refinement.

For the case of adaptive refinement I would suggest to not use this WENO implementation as it would require some structural changes of the code and also would be VERY slow.

I do not know of any WENO implementation that can handle unstructured grids, e.g. cells with any shape, that also handles adaptive mesh refinement. I think the best performance would be to use a hybrid scheme with a shock detector. Thus, to get at least perfect second order in the smooth region and then to fall back to either upwind or limitedLinear at the shock.

However, the shock sensors require some tuning to your case so they do not set everything to upwind or have to little smoothing. But if you have only one case you simulate you can tune it for this particular case.

A possible shock detector is explained in here:
[1] Ducros, F., Ferrand, V., Nicoud, F., Weber, C., Darracq, D.,
Gacherieu, C., & Poinsot, T. (1999).
Large-eddy simulation of the shock/turbulence interaction.
Journal of Computational Physics, 152(2), 517-549.

October 21, 2020, 15:41	Effcient WENO Scheme	#1
janGaertner New Member Jan Gaertner Join Date: Nov 2017 Posts: 17 Rep Power: 8	Hello all, in the recent months I had put a lot of work into the WENO Scheme originally written by Tobias Martin to improve efficiency and computational speed. It has finally reached a state that is stable and has proven to reach the accuracy and performance that I would expect from this scheme. This has been now also published in SoftwareX describing some of the improvements and the test cases (https://doi.org/10.1016/j.softx.2020.100611). If you are looking for a higher order scheme which also works for discontinuities in flows, such as shocks, this would be a good choice. Please check it out on GitHub https://github.com/WENO-OF/WENOEXT Hope some of you will find it helpful (If you find any bugs or have ideas how to improve it please send me an e-mail or open an issue) li siye likes this.

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November 5, 2020, 07:17		#2
janGaertner New Member Jan Gaertner Join Date: Nov 2017 Posts: 17 Rep Power: 8	Hello, I am sorry to say that there was a major bug in the latest release of the library. In the release 2.0 the integer power multiplication for the Gauss quadratur was incorrect for any order higher than 2. Sadly this mistake did not appear in any of my small test cases. However, the release 1.0 which is used for the publication is correct. I have now fixed this error and released 2.1 version which should fix this issue.

December 7, 2020, 09:11		#3
li siye New Member Join Date: Oct 2020 Posts: 10 Rep Power: 5	Thank you for your amazing jobs! Jan Gaertner! I have a big problem that if i use dynamicRefineFvMesh (AMR method), how can i also use the WENO library to get the stencil where the level and size of cells are different, how can deal with this problem. Thanks a lot again! Best wishes to you!

December 8, 2020, 04:33		#4
janGaertner New Member Jan Gaertner Join Date: Nov 2017 Posts: 17 Rep Power: 8	Hello Siye, the calculation of the stencil list and corresponding matrices is computationally very expensive. Therefore, it is currently implemented to be done only once when the scheme is called the first time, after this the matrix and stencil lists are stored as a static object. Thus, you cannot recreate this list at run time, which conflicts with adaptive mesh refinement. For the case of adaptive refinement I would suggest to not use this WENO implementation as it would require some structural changes of the code and also would be VERY slow. I do not know of any WENO implementation that can handle unstructured grids, e.g. cells with any shape, that also handles adaptive mesh refinement. I think the best performance would be to use a hybrid scheme with a shock detector. Thus, to get at least perfect second order in the smooth region and then to fall back to either upwind or limitedLinear at the shock. However, the shock sensors require some tuning to your case so they do not set everything to upwind or have to little smoothing. But if you have only one case you simulate you can tune it for this particular case. A possible shock detector is explained in here: [1] Ducros, F., Ferrand, V., Nicoud, F., Weber, C., Darracq, D., Gacherieu, C., & Poinsot, T. (1999). Large-eddy simulation of the shock/turbulence interaction. Journal of Computational Physics, 152(2), 517-549.