Application of a Novel High-Order WENO Scheme in LES Simulations

Round 1

Reviewer 1 Report (New Reviewer)

Comments and Suggestions for Authors

see attached file 

Comments for author File: Comments.pdf

Comments on the Quality of English Language

Moderate technical English editing is recommended

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

In this paper, the authors presented a numerical work in which a high-order finite volume weighted essentially non-oscillatory (WENO) scheme for large eddy simulation (LES) is developed in this study, which is embedded into the three-dimensional viscous unsteady computational fluid dynamics (CFD) solver NUAA-Turbo. So far, the main contribution of this paper is that the application of new WENO scheme, which is a convex combination of a high-degree polynomial and multiple linear polynomials. Moreover, they argued that this scheme achieves optimal high-order accuracy in smooth regions containing complex numerical solution structures while suppressing spurious oscillations near strong discontinuities, and comparing to the classical WENO scheme, the new scheme eliminates the computation of nonlinear weights highly dependent on grid shape, reducing computational cost and preventing calculation crashes caused by negative nonlinear weights. And the results revealed that the new WENO scheme has smaller dispersion and dissipation errors, faster convergence speed, and better analytical ability for high-frequency waves. Moreover, the new WENO scheme captures flow structures with good shock wave capture ability and turbulence resolution. It can capture richer flow field details with the same grid and requires fewer grid points to achieve the same accuracy, which lays a foundation for high-precision LES large-scale engineering application of compressible turbulence flow. Here it should be mentioned that the paper is well presented, and the novelty of this paper is well stated.   

Author Response

We would like to express our sincere gratitude to the reviewer for their thorough evaluation and for acknowledging the quality of our work. We appreciate the time and effort you have invested in reviewing our work.

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

The subject covered is interesting and relevant. The study has some potential
for publication, but many details related to the simulations are missing,
which initially invalidates publication. I also suggest a deeper and more
comprehensive discussion of the results. I recommend that the paper be
rejected and may be analyzed again in the future if the suggestions below
are implemented.

 

1) In "References" there are words incorrectly separated between lines. For example in Ref [1]: end of first line "hig" followed by "h" in the second line. I suggest a carefull review of "References" texts.

2) Lines 38 and 39: "...while minimizing computational costs...". Actually LES has much more costs than RANS, for example. So, this "minimizing" is related to what?

3) Line 77: the author of Ref [24] is only "Sheng", not "Zhong".

4) Line 79: duplicated "25".

5) Line 93: Avoid using the first person like in "... we can ...". The same in lines 99, 101, 103, 105 and others.

6) Line 112: remove "In". I suggest: "Section 4 concludes with final remarks."

7) Line 151: are you sure that Refs. [30,31] are related to the adaptive formula? Because they seems to be related to turbines and hydropower.

8) Why do you set "epsilon=10e-6"? Why this value? Comment more on this.

9) Lines 174 to 179: Comment more about the NUAA-Turbo. Do you have references explaining this solver?

10) Line 327: start with upper case letter "The".

11) Line 329: respectively?

12) Line 333: Why 307 K? Comment more on this.

13) Show in the Figure 11 the three directions: s, y, and z.

14) Line 344: wrong empty space in "law".

15) Figure 16: "LES" is the WENO-ZQ5?

16) Did you do the mesh dependence study? I recommend to show it. If you didn't do it, this represents a Major Problem of the study.

17) Regarding all your unsteady simulations: what time steps were used? Did you do the time step sensitivity study? If not, this is also a problem.

18) I recommend to add figures showing the turbine domain and its mesh.

19) I recommend to show the residual decayment of all simulations? What about simulations total time? In what computer did you simulate the cases?

20) I think that is missing a deeper discussion about the results.

Comments on the Quality of English Language

I suggest a moderate English language review.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report (New Reviewer)

Comments and Suggestions for Authors

see file attached

Comments for author File: Comments.pdf

Comments on the Quality of English Language

N/A

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

Most suggestions have been implemented and the quality of the paper is higher.

However, I emphasize that comment 19 was not fully attended. For the case "Pakb Cascade", it was informed that the simulation takes 1 month. However, the total simulation times of other cases are still missing.

Regarding comment 16, more information was provided, especially with regard to YPlus, which is good. However, the doubt has not yet been answered: if the meshes are more or less refined, what will happen with the results? This is important to ensure independence of results in relation to spatial discretization, as well as to ensure the reliability of the numerical scheme. Although the results are close to the experimental, this does not guarantee that the method is appropriate.

I recommend don't publisinhg the paper until the above points are explained.

Author Response

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Author Response File: Author Response.pdf

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors present discretisation schemes for numerical simulation of turbulent flows. The manuscript focuses on WENO schemes, which are especially used in high-speed flows with discontinuities, such as shock waves. The schemes are applied to different simple test cases.

The novelty of the content is questionable. It is not clear which part is new and which is just stand-of-the-art. Thus, the quality of the submission cannot be judged.

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Figure 18 c should have a colour bar.

The iThenticate report shows a match of 46%.

Comments on the Quality of English Language

The use of the language should be improved. For example, "This scheme enables the use of fewer grids, ...". The authors mean mesh cells and not grids.

Author Response

Please see the attachment.

 

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The document requires a series of modifications:

- In the abstract, it would be beneficial to specify in more detail the specific benefits of the new WENO scheme compared to classic schemes, beyond just reduced computational costs. Including quantitative data on improvements in accuracy or efficiency could strengthen this section. The phrase "enables the use of fewer grids" could be more specific by indicating a percentage or a direct comparison with traditional methods. The claim "enhances robustness and stability" needs concrete evidence or references to results that support this assertion.

- When describing and justifying the employed methodological approach, you could mention previous works that used fuzzy logic to model complex phenomena in dynamic systems, including turbine simulation. I recommend searching for information on the following topics in this section:

  a) Viability Analysis of Tidal Turbine Installation Using Fuzzy Logic: Case Study and Design Considerations

  b) Revitalizing the Canal de Castilla: A Community Approach to Sustainable Hydropower Assessed through Fuzzy Logic

- The method for validating input data for simulations is not mentioned, which could question the veracity of the results.

- The description of the coefficient calibration method is insufficient and lacks details on the criteria used for its adjustment.

- Use of graphs without proper labels on the axes or clear legends, which can confuse the reader.

- Discussion of the results without mentioning confidence limits or error intervals, which is crucial in simulation studies to validate accuracy.

- The conclusions do not directly relate to the initially stated objectives, which makes it difficult to follow the logic of the study's impact. Use of overly general language that does not reflect the specific results of the study; for example, terms like "excellent capability" should be supported by quantitative data.

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

Reviewer compliments authors on their thorough investigation as the improvement of WENO scheme for LES flow modelling is of great importance. However, the authors should consider the following remarks in their next revision.

General remarks
1. A few statements are rather strong and unsupported. E.g. page 7, lines 206-208: ."...it becomes evident that..." is stating something evident to the authors but to the reader it might not be. Authors should provide additional references to support their claims.
2. Some figures should be of higher quality. E.g. Figure 16 resolution should be increased.
3. Some figures are missing legends. E.g. Figure 1a contains a legend while Figure 1b doesn't. It is clear to me that both Figures use the same legend so authors might consider to have them in both figures.
4. All comparisons in the results section should have some numerical goodnes-of-fit.
5. In conclusions section, in line 490, authors state that "...new WENO schemes can reduce computational cost by using fewer grid cells...". Are there any results to support this claim?

Specific remarks
1. Page 3, line 127: "...cedures narrated latter." is out-of-place. Please, remove it or correct it.
2. Page 6, equation number 20 appears two times. Authors should correct it and numbering to all subsequent equations.
3. Page 7, line 212: what are strategies? Authors should use some more appropriate word.
4. Page 9, lines 285-287 state that C_w = 0.45 was selected based on a lot of experiments. Authors should cite some of their previous work to support this statement.
5. Page 17, line 440: "...which is a typical high-load..." Authors should support this claim using a relevant reference.
6. Section 3.3 presents results using WENO-ZQ5 scheme. While other comparisons include WENO-JS scheme, have authors considered to to the same for "Pak B Low Pressure Turbine Cascade" example?
7. Figure 18c is missing a scale for the range of coloured values.

Comments on the Quality of English Language

Article is nicely written and readable to non-native English speakers.

Author Response

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Author Response File: Author Response.docx

Reviewer 4 Report

Comments and Suggestions for Authors

The paper proposes a new WENO scheme for LES simulation that enhances computational efficiency and accuracy. The paper is well-organized and reads well. I only have some comments that I would like to be addressed in the revised manuscript

1.       There are four references in Chinese, which makes it difficult for broader readers to follow the paper. They can be kept but along with similar reference in English.

2.       When an abbreviation is used for the first time, its full term must be included. See examples: (Line 58, WENO; Line 63, JS; Line 81, ZQ; Line 271, WALE; Line 277, AUSM-up, etc.).

3.       Line 60: Define “r”.

4.       There is a typo in Line 127: “… cedures narrated latter.”

5.       Present the comparison quantitatively. It would be good to use error quantifiers such as RMSE or NRMSE.

6.       Fig. 4 can be discussed better by comparing the weaknesses and strengths of each model. Both models seem to have good efficiency in modelling the turbulent energy spectrum. What is the advantage of WENO-ZQ over WENO-JS in this figure?

7.       In the discussion on Fig. 10: “… WENO-ZQ scheme is closer to the reference solution.” Use a quantifier to specify how much closer.

8.       The performance of WENO-ZQ and WENO-JS is qualitatively compared in various figures; however, there is no quantitative comparison showing how much improvement was obtained using the WENO-ZQ approach compared to WENO-JS. This must be reflected in the abstract and conclusion sections.

9.       Computational efficiency is touched upon in Fig. 9; however, it must be further discussed in terms of both convergence and computational time. This must be reflected in the abstract and conclusion sections.

Comments on the Quality of English Language

There are four references in Chinese,

Author Response

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Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have made all the requested modifications