Comparing Darcy’s Law and the Brinkman Equation for Numerical Simulations of Saltwater Intrusion

Round 1

Reviewer 1 Report

The paper presents a comprehensive comparison between Darcy's Law and the Brinkman Equation in the context of saltwater intrusion simulations in coastal aquifers. The study evaluates the performance and accuracy of both models in capturing density-driven flows, particularly in situations involving dispersive mixing. The study provides some valuable insights into when and why the Brinkman Equation should be utilized, especially in scenarios involving complex flow patterns and geological conditions. However, there are some problems that should be solved before acceptance.

 

1. The abstract could be enhanced by including specific numerical outcomes or percentages to highlight the magnitude of discrepancies.

2. The implications of the research for practical applications could be further emphasized in the discussion.

3. In what ways did the Brinkman Equation demonstrate superiority in capturing intricate flow patterns and variations?

4. Could you provide more details about the procedure used to evaluate the impact of the Laplace term in the Brinkman Equation?

5. Line 375: How were density and velocity variations accounted for during the break-through period and within the dispersion zone?

6. Could you discuss the computational efficiency of both equations, especially in larger-scale simulations?

7. Can you explain how the study's conclusions extend to other complex geological conditions beyond saltwater intrusion?

 

Minor editing of English language required

Author Response

Dear reviewer, 

Thank you for taking the time to review this manuscript. We have taken your constructive feedback into consideration and addressed all the comments. Please see the attachment for the detailed response and revised manuscript. 

Regards

Author Response File: Author Response.pdf

Reviewer 2 Report

Ms. Ref. No.: sustainability-2572854

Title: Comparing Darcy’s Law and the Brinkman Equation for Saltwater Intrusion Simulations

 

 

The aim of this paper, evaluate under what circumstances the Brinkman Equation is required. To achieve this, numerical simulations with both models were implemented in hypothetical coastal aquifer scenarios. The impacts of parameters including hydraulic conductivities, recharge rates and tidal fluctuations were assessed. Results reveal that the largest discrepancies occur inside the dispersion zone during the break-through period. The mixing of fresh and saltwater induces rapid changes of densities and velocities. Brinkman’s viscous term moderates the rate of change and results in a less intrusion extent than Darcy’s Law. Furthermore, a higher permeability and a lower recharge rate both strengthen the viscous effects.

I, recommend this paper be published in the Sustainability Journal after the authors address the following comments.

 

·         Review English grammar as there are mistakes throughout the text.

·         5 lines of the abstract are extra. Remove these lines.

·           The resolution of figures must be improved. Such as figure 2?!!

• The physical explanation of figures 9 and 11 is limited. Please explain more
• More physical insight into the results section is needed.
• The author needs to provide quantitative results and qualitative results in the abstract section of the article so that the reader can understand the generalities of the presented article.
• Add a section on study limitations before the conclusion section.
• The conclusion is too long and so weak. Please explain your main findings quantitatively.
• The author must improve the introduction with more advanced applications. Also, the author could find new references and review these articles for CFD and equations. The authors read these articles: https://doi.org/10.20886/ijfr.2017.4.2.151-168, https://doi.org/10.1002/ceat.202300102

 

In conclusion, this paper might be made suitable for publication in this Journal if the as-mentioned comments are clarified. These constitute a Major revision of it.

Minor editing of English language required

Author Response

Dear reviewer, 

Thank you for taking the time to review this manuscript. We have taken your constructive feedback into consideration and addressed all the comments. Please see the attachment for the detailed response and revised manuscript. 

Regards

Author Response File: Author Response.pdf

Reviewer 3 Report

Manuscript ID: Sustainability- 2572854

Title: Comparing Darcy’s Law and the Brinkman Equation for Salt-water Intrusion Simulations

 

Dear Authors

This manuscript presents an investigation into saltwater intrusion in a tidal-driven coastal aquifer using the finite-element modelling package, COMSOL Multiphysics. While the results obtained are intriguing, there are major revisions required before considering publication in the Journal of Sustainability. The author(s) are advised to address the following suggestions to improve their work.

 

1.     Mesh independence should be investigated to determine if the results of a numerical simulation are not significantly affected by changes in the mesh size or density. It is an important step in validating the accuracy and reliability of a simulation.

2.     Address any limitations or assumptions made in the study and suggest areas for future research.

3.     Investigate the sensitivity of the results to various parameters, such as boundary conditions, mesh size, turbulence models, or other model inputs. This helps assess the robustness and reliability of the simulation.

4.     Add more flow visualization (contour plots, streamlines, velocity vectors, pressure distributions, etc.) to provide insights into the flow patterns and help readers understand the flow behavior.

5.     Detail the numerical methods employed in the simulation, such as discretization schemes, solution algorithms (e.g., explicit, implicit), and any sub-models used.

6.     Evaluate the computational performance of your CFD simulation, such as the computational time, memory usage, or parallel scalability.

7.     Assess the convergence of your solver by monitoring the solution residuals. Show that the solution has reached a steady state or a converged solution, indicating that the numerical solution is stable and reliable.

 

 

 

 

Sincerely yours,

Moderate editing of English language required

Author Response

Dear reviewer, 

Thank you for taking the time to review this manuscript. We have taken your constructive feedback into consideration and addressed all the comments. Please see the attachment for the detailed response and revised manuscript. 

Regards

Author Response File: Author Response.pdf

Reviewer 4 Report

This research focused on evaluating under what circumstances the Brinkman Equation is required. The reviewer believes that the current version of the manuscript is not yet ready for publication; the authors are encouraged to consider the following comments and suggestion and revise the manuscript accordingly.

1. The authors should consider improve the Introduction section. The authors should split the Introduction sections into to two sections, including an introduction section and a background section. The introduction section should focus on introducing the research objectives and research questions, while the Background section should focus on literature review of related work and discussing why a review paper is important on this subject. The authors should also review more related literature.

2. The authors should review the equations to make sure all symbols have been appropriately denoted. In addition, a document should be provided to further explain the equations. Additionally, the authors should provide more information about the software or codebase that were used to achieve the proposed image processing algorithms.

3. The authors need to provide detailed information about the parameters and their values. How were the values being collected?

4. Most of the figures need to be revised to make them more legible. It is very blurry and hard to read. If at all possible, vector images should be used.

N/A

Author Response

Dear reviewer, 

Thank you for taking the time to review this manuscript. We have taken your constructive feedback into consideration and addressed all the comments. Please see the attachment for the detailed response and revised manuscript. 

Regards

Author Response File: Author Response.pdf

Reviewer 5 Report

Please read the attached file for details.

Comments for author File: Comments.pdf

Please read the attached review comment for details.

Author Response

Dear reviewer, 

Thank you for taking the time to review this manuscript. We have taken your constructive feedback into consideration and addressed all the comments. Please see the attachment for the detailed response and revised manuscript. 

Regards

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The manuscript has been modified by the author in accordance with the suggestions provided.

After careful consideration, I am pleased to state that I am satisfied with the modifications made by the author. 

Reviewer 2 Report

Accept

Reviewer 3 Report

Dear Authors

I hope this letter finds you well. I am expressing my satisfaction with the revised version of the manuscript titled Comparing Darcy’s Law and the Brinkman Equation for Saltwater Intrusion Simulations" (Manuscript ID: sustainability-2572854), which has been thoroughly reviewed by the assigned reviewers. I am pleased to inform you that the authors have diligently addressed all the comments and suggestions raised by the reviewers, resulting in a significantly improved manuscript.

Yours sincerely,

Moderate editing of English language required

Reviewer 4 Report

The authors have addressed all my comments.

N/A

Reviewer 5 Report

The revised manuscript is good for publication.