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楼主: linf1017

High order shock-capturing TENO (targeted ENO) schemes

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 楼主| 发表于 2018-10-4 05:00:33 | 显示全部楼层
coolboy 发表于 2018-9-28 22:11
Thanks for sharing the information.
What is your opinion on the scheme by Colella and Woodward (Pie ...

Well. Piecewise Parabolic Method has been popular for many long time, particular for astrophysical simulations.

However, this type of schemes may still need some sort of adhoc operator for dicontinuity capturing,
e.g. see Eq.(3.2) in

https://cloudfront.escholarship. ... 07f1/qt5sr307f1.pdf

As far as I know, the ENO family scheme may be the state-of-the-art in terms of high-order accuracy, and sharp shock-capturing capability. The main drawback of previous version , e.g. WENO, is that they are typically very dissipative either.

This problem is greatly fixed by the concept of TENO.
发表于 2018-10-8 00:56:59 | 显示全部楼层
Thanks a lot.
 楼主| 发表于 2018-10-21 12:35:28 | 显示全部楼层
Recently, I propose low-dissipation finite-volume method based on a new TENO shock-capturing scheme:

https://www.sciencedirect.com/sc ... i/S0010465518303576
 楼主| 发表于 2018-11-10 16:01:10 | 显示全部楼层
The five-point and six-point TENO schemes are further improved to the performance limit of optimal linear schemes

https://www.researchgate.net/pub ... daptive_dissipation

 楼主| 发表于 2019-1-8 07:39:04 | 显示全部楼层
I propose "A hybrid method with TENO based discontinuity indicator for hyperbolic conservation laws" :

https://www.researchgate.net/pub ... c_conservation_laws

which reduces the computational costs of TENO scheme significantly.


1. With the observation that the TENO weighting strategy can explicitly distinguish smooth scales from nonsmooth scales in spectral space, in this paper, a new troubled-cell indicator is proposed based on the high-order TENO paradigm.
2. The cut-off wavenumber separating smooth and nonsmooth scales is determined by the parameter C_T. In contrast to the thresholds of other troubled-cell indicators, which are typically defined in physical space, C_T takes effects in wavespace rendering its high generality.
3. The local flow structures are classified as smooth or nonsmooth scales, and the hybrid numerical discretization scheme is applied correspondingly, i.e. the high-order upwind linear scheme without characteristic decomposition is employed for resolving smooth scales while the nonlinear low-dissipation TENO scheme is adopted to capture discontinuities.
4. A set of benchmark cases with widespread length-scales is simulated to assess the performance of the proposed troubled-cell indicator and the resulting hybrid shockcapturing scheme.
5. The parameter is not tuning for all simulations.
 楼主| 发表于 2019-3-9 03:09:22 | 显示全部楼层
One review about High-order TENO Schemes for Hyperbolic Conservation Laws can be found in

https://www.researchgate.net/pub ... c_Conservation_Laws
发表于 2019-5-10 20:45:08 | 显示全部楼层
不错,学习一下
 楼主| 发表于 2019-5-25 02:17:54 | 显示全部楼层
Thanks to the work of Nico Fleischmann, the low-dissipation property of TENO schemes is demonstrated with extreme resolution simulations and the symmetry breaking issue has been addressed:

https://www.sciencedirect.com/sc ... i/S0045793018308399

e.g.

TENO scheme

TENO scheme
 楼主| 发表于 7 天前 | 显示全部楼层
The low dissipation TENO6 scheme for Rotor Wake simulations
Thanks to the work of Constantin Oehrle, the low-dissipation TENO6 scheme has been implemented in the DLR block structured finite-volume Reynolds-averaged Navier-Stokes (RANS) CFD code FLOWer. The performance is impressive (in their paper called WENO6 scheme):

https://www.researchgate.net/pub ... ive_Mesh_Refinement

TENO6_aerodynamics.png
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