High order shock-capturing TENO (targeted ENO) schemes

coolboy

Thanks for sharing the information.
What is your opinion on the scheme by Colella and Woodward (Piecewise Parabolic Method), for P. Colella is also at UC Berkeley.

coolboy

Thanks a lot.

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?

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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