A Review of Topology Optimisation for Fluid-Based Problems

Round 1

Reviewer 1 Report

The reviewer feels this manuscript is well written and organized as the first review paper of research on fluid topology optimization. Before recommending publication, the reviewer requests the authors to respond the following comments.

<1> p.8, line 347, "[94]applied" --> "[94] applied"

<2> p.14, caption of fig.4
More detailed informations should be provided, e.g., keywords for searching, and website (Scopus?).

<3> p.14, line 502, 1'2 --> 182

<4> p.15, line 613, "such as the Method of Moving Asymptotes"
Since the first-order methods are popular in fluid topology optimization, the authors should provide more detailed descriptions. For instance, SLP, SNOPT, IPOPT etc. are used in the papers on fluid topology optimization. The reviewer recommends to add the circle graph, similar with fig.5, for the optimization methods.

<5> p.15, line 610, "However, gradient-free..."
The reviewer agrees with the authors opinion, but the authors should add the description of their advantage for multi-objective problems.

<6> p.16, line 635, "stabilised FEM has ... accurate method"
The evidential literature should be provided.

<7> p.19, line 697, "objective functional with respect to the design variable"
In the reviewer's opinion, the "objective functional" should be used in continuous formulation, while the "design variable" should be used in discrete formulation. In the continuous formulation, the material distribution corresponding to design variable is expressed as ρ(x) which is the "function" of position x. The reviewer recommends the authors to modify the text as "objective function with respect to the design variable".

<8> p.19, Section 4.2
Since Section 4 is "Recommendations", the authors should provide any recommendation here.

<9> p.19, line 729, "Future papers..."
The authors should provide more recommendations. Since the steady-state laminar flow problems are the most popular and the versatile fields in fluid topology optimization, for instance, practical engineering applications are to be future research topics.

<10> p.20, line 743, "In extension..."
This paragraph is unclear what the authors want to state. Please describe more clearly.

<11> p.20, Section 4.6
The reviewer considers that directly solving turbulent problems by topology optimization is important, but also consider that indirect approaches such as the poor man's approach are important for solving such complex topology optimization problems. If the authors agree with that, please add this comment as a recommendation.

<12> p.23-24, references
There are many typos, e.g. stokes --> Stokes.

Author Response

We wish to thank the reviewer for the kind words and insightful comments. Based on the comments of the reviewer, we have rewritten and added several passages in the text. Simple corrections have been marked in blue and significantly revisions have been marked in red. Furthermore, due to copyright issues, Figure 3 has been remade from scratch.

1) Corrected.
2) Section 1.1.2 has been added to describe the literature search.
3) Corrected.
4) The subsection on optimisation methods has now been moved to the Ssection 4.1 in the Recommendations section. As the aim of the review is not to go into specifics about the gradient-based optimisation algorithms, we have removed the specific reference to the MMA algorithm, rather than go into more detail as suggested by the reviewer.
5) The subsection on optimisation methods has now been moved to the Ssection 4.1 in the Recommendations section. We are not aware of any significant benefits of applying gradient-free methods to multi-objective problems, compared to using a Pareto-front exploration of a weighted sum objective using gradient-based approaches, see e.g. reference [125] of the manuscript. However, a short comment has been added to what is now Section 4.1.
6) Two references [194,195] have been added to support the argument.
7) We do not fully agree with the reviewer, as a functional is defined as a mapping from a vector space to a real scalar, which is also the case in the discrete setting. However, the authors would like to be as general as possible (continuous) and have instead changed the sentence to ``objective funcitonal with respect to the design field''.
8) Section 4.3 has been rewritten to make more clear recommendations.
9) An additional sentence has been added in order to clarify the importance of treating practical engineering applications.
10) The paragraph has been rewritten to make the arguments more clear.
11) This is already discussed in Section 4.11 dedicated to simplified models, but a sentence has been added about this to Section 4.7.
12) We have to the best of our ability fixed any typographical errors in the references.

Reviewer 2 Report

The manuscript contains a review of 186 articles selected by the authors in the field of fluid-related topology optimization, which were published from 2003 to the beginning of 2020.

The authors made several classifications of topics covered in the above-mentioned articles and based on them conducted an in-depth analysis of the data obtained in this way in order to identify trends in this field, which they then included in the conclusions.

The paper contains an up-to-date compendium of knowledge in the field discussed and thus constitutes a valuable source of information for scientists and engineers in the fluid industry.

The manuscript is clearly written and its form is aesthetic and is suitable for publication without any changes.

Author Response

We wish to thank the reviewer for the kind words and appreciation for our work. According to the comments of the Reviewer 1, some changes have been made from the initial submission. Simple corrections have been marked in blue and significantly revisions have been marked in red. Furthermore, due to copyright issues, Figure 3 has been remade from scratch.