High order shock-capturing TENO (targeted ENO) schemes

linf1017

A new hypersonic flow solver from Center for Turbulence Research at Stanford University is published. The solver is based on the sixth-order low-dissipation TENO6-A scheme for shock-capturing and the code is open-source:

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

https://www.sciencedirect.com/sc ... i/S0010465520300837

linf1017

Thanks to the work of Arash Hamzehloo and his team, the TENO schemes are demonstrated to perform significantly better than WENO for compressible wall-bounded turbulence:

https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.4879

linf1017

Glad to give an invited seminar talk on the high-order TENO schemes for general hyperbolic conservation laws and turbulent flows

High-order TENO schemes for general hyperbolic conservation laws and turbulent flows

周华

linf1017 发表于 2020-7-1 10:17
Glad to give an invited seminar talk on the high-order TENO schemes for general hyperbolic conservat ...

讲的很好，很受启发

linf1017

周华 发表于 2020-7-1 13:21
讲的很好，很受启发

感谢 周老师 的支持！

linf1017

Open-source codes based on the high-order TENO schemes for complex fluids:

OpenSBLI solver

Based on TENO5, TENO6 and TENO8

A framework for the automated derivation and parallel execution of finite difference solvers on a range of computer architectures.

Lusher, David J., Satya P. Jammy, and Neil D. Sandham. “OpenSBLI: Automated code-generation for heterogeneous computing architectures applied to compressible fluid dynamics on structured grids.” arXiv preprint arXiv:2007.14933 (2020).

Code repository, https://github.com/LMNS3d/opensbli

HTR solver

Based on TENO6-A

An open-source exascale-oriented task-based multi-GPU high-order code for hypersonic aerothermodynamics

Renzo, Mario Di; Fu, Lin; Urzay, Javier; “HTR solver: An open-source exascale-oriented task-based multi-GPU high-order code for hypersonic aerothermodynamics,” Computer Physics Communications, (2020): 107262.

TENO scheme and HTR solver have supported the DOE PSAAP 3 (Predictive Science Academic Alliance Program) project at Stanford University, link for psaap 3 at stanford.

Code repository, https://data.mendeley.com/datasets/9zsxjtzfr7/1

ALPACA solver

Based on TENO5

A MPI-parallelized C++ code framework to simulate compressible multiphase flow physics

Hoppe, Nils; Adami, Stefan; Adams, Nikolaus A. ; “A modular massively parallel computing environment for three-dimensional multiresolution simulations of compressible flows,” arXiv:2012.04385, (2020).

Code repository, https://gitlab.lrz.de/nanoshock/ALPACA

MPI-AMRVAC solver

Based on TENO5-A

MPI-AMRVAC: A Parallel Adaptive Mesh Refinement Framework

van der Holst, Bar, et al. “MPI-AMRVAC: MPI-adaptive mesh refinement-versatile advection code,” Astrophysics Source Code Library (2012): ascl-1208.

Code repository, https://github.com/amrvac/amrvac

linf1017

We are moving towards the next generation high-order low-dissipation TENO schemes for solving nonlinear PDEs, see our latest paper on Journal of Computational Physics:

A novel high-order low-dissipation TENO-THINC scheme for hyperbolic conservation laws

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

https://www.sciencedirect.com/sc ... 21007944?via%3Dihub

coolboy

linf1017 发表于 2021-12-21 22:50
We are moving towards the next generation high-order low-dissipation TENO schemes for solving nonlin ...

Nice work and impressive numerical results!

“The weights w_k are computed dynamically by the TENO weighting strategy such that the Gibbs phenomenon in proximity to the discontinuities are avoided while the high-order accuracy in smooth regions is restored.”

This above statement looks very interesting but I have difficulty to figure out how it was implemented according to the statement while designing the schemes. “Gibbs phenomenon” involves spectral or Fourier expansion whereas the functional form near the shocks was assumed to be a polynomial form as shown by Eq. (6). Is this the central idea of avoiding the Gibbs phenomenon?

linf1017

The original idea of TENO is to avoid the Gibbs phenomenon by avoiding the reconstruction crossing the discontinuities.

In this new idea, the discontinuity is indeed resolved by the THINC scheme instead of capturing.

You can figure out the code implementation in a set of open-source codes based on TENO:

http://linfu.people.ust.hk/open-source-codes.html

coolboy

You might be interested in knowing the following blog article with my comments below because it mentioned Chi-Wang Shu（舒其望）who is an expert in your field.
I am not familiar with your field but I am curious and like to ask you a question and hopefully get your opinion on my question (if you do not mind to answer):

What do think on the academic aptitude on Chi-Wang Shu in comparison with Peter Lax? Suppose we scale the academic aptitude from 0 to 9 and put Peter Lax on level 7. Then, which level do you think will Chi-Wang Shu be placed on?

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谈谈世界顶尖科学家的排名榜
https://blog.creaders.net/u/9037/202203/429771.html

coolboy:
看到Jerrold E. Marsden的名字，书架上有他合著的几本书。他应该算是一位数学力学家。
问好博主。出过专著和教科书的作者一般都会有很高的引用率。然而，专著和教科书的出版其实并不用经过严格的审稿程序。
根据博主以前的博文推测，上列数学家以及他们的研究中，博主最熟悉的一位应该是Chi-Wang Shu（舒其望），属于计算数学。
对于绝大多数的应用工作者来讲，他们通常不大看原始论文，也不关心前沿发展，而是查看以及引用专著或教科书。舒其望教授研究领域的结果我其实也时常用到。但我常翻看、使用以及引用的相关文献则是这本书：Laney, C. B., 1998: Computational Gasdynamics. Cambridge Univ. Press, Cambridge, 613 pp.
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