High-Order CFD Solvers on Three-Dimensional Unstructured Meshes: Parallel Implementation of RKDG Method with WENO Limiter and Momentum Sources

Round 1

Reviewer 1 Report

The authors of this article follow up on their previous work; they use a developed solver to study inviscid compressible flows on unstructured three-dimensional meshes. My suggestions to improve the quality of the manuscript are listed below. Please include all responses in the manuscript. 

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript entitled High-order CFD Solvers on Three-dimensional Unstructured Meshes: Parallel Implementation of RKDG Method with WENO Limiter and Momentum Sources is numerical study of Parallel Implementation. I commented as follows;

 

1.The author should revise the reference in Line 56.

2.Introduction is not clear. The author should revise it. Especially, disadvantages of the previous studies and advantages of the present study should show.

3.The validity of the numerical results is very important. The author should compare with the experimental results or the previous results in other numerical methods.

4.The many letters and symbols are used. The author should summarize them as a nomenclature.

Author Response

Thanks for the comments. Here is our point-by-point response:

1) It has been fixed now in the revised version. Sorry for forgetting updating the bibtex database before submission.

2) Besides the parallel implementation of the RKDG method with WENO limiters, the main contribution of this paper is the finite-element/momentum-source hybrid method. It overcomes the drawbacks of previous studies, which are either over simplified by ignoring unsteady effects, or restricted to structured meshes. We have revised the introduction to show this novelty.

3) Yes, we do have validated the numerical results, although not extensively. The main purpose of Section 3.1 is to validate the correctness and measure the accuracy of the solvers implemented by us. The shock tube problems in this section have exact solutions, which are ideal for measuring the accuracy of numerical solutions. The forward step problem in this section has no exact solution, but its numerical solutions published in literatures all converge to the same flow pattern. Such a consensus on its solution makes it a model problem for testing multi-dimensional shock capturing methods. Results of these model problems, together with those presented in our previous work, validate the correctness of the solvers either quantitatively or qualitatively. In Sections 3.2 and 3.3, real three-dimensional problems in aeronautical engineering are solved, and comparisons between first- and third-order RKDG solutions are given. Mathematically, first-order RKDG solutions are equivalent to traditional (first-order) finite volume solutions, which are highly reliable and thus are used for validating our third-order RKDG solutions.

4) Thanks for the suggestion. We add a symbol table after the section of abbreviations.

Reviewer 3 Report

In the abstract, it looks like the main work of this paper is to implement a mature method in different scenarios. The novelty of this paper should be further cleared. For instance, what is the exact scientific challenge of using the previous methods to solve the new problems?

In the introduction, the authors refer to their own early works like ‘in our early works’. But no reference is provided here.

A reference is missing following ‘Kang and Sun [??]’ in the last paragraph of the introduction.

A more specific section title is preferred for section 2, instead of a too ambiguous one ‘methods’.

 

It is seen from the analysis that the numerical accuracy increases with the increase of p. But it is not clear how much performance is improved with respect to the previous ones. Could you please include more comparative analysis with other methods to claim the superiority of this method?

Author Response

Thanks for the comments. Here is our point-by-point response.

1) We admit that the RKDG method with WENO limiters is proposed by other scholars. Our work is to provide an efficient parallel and open-source implementation of it and test the implemented solvers on three-dimensional unstructured meshes. The second contribution of this paper is the finite-element/momentum-source hybrid method, which is our first attempt to augment the RKDG/WENO method. We have revised the abstract to show this novelty.   2) One of our recently published paper has been added.

3) Sorry for forgetting updating the bibtex database before submission. It has been fixed now in the revised version.

4) The section titles have been revised.

5) Thanks for the suggestion. We add some data and discussion to show that high-order solvers are better than low-order ones.

Round 2

Reviewer 1 Report

The authors addressed all the comments precisely and thus the paper can be accepted in its current form.

Reviewer 2 Report

The author's revisions are satisfied.