A Cartesian Method with Second-Order Pressure Resolution for Incompressible Flows with Large Density Ratios

Round 1

Reviewer 1 Report

The work carried out in this article is very interesting,in the sense that it improves the performance of the results
concerning bi-fluids with large difference in density.
So I find that this is a job that is largely well done to be accepted for publication.
However, I recommend that this minor remark be taken into account in the final writing of the article: In the summary of the article, it is desirable to mention that the work is based mainly on the improvement of the Ghost-Fluid method.

Author Response

First of all, we want to thank both reviewers for their careful work that helps us to improve the manuscript.

We detail in the following what we have done to answer their remarks

Reviewer 1: 
-« However, I recommend that this minor remark be taken into account in the final writing of the article: In the summary of the article, it is desirable to mention that the work is based mainly on the improvement of the Ghost-Fluid method. »

According to the recommendation of the reviewer, we mentionned in the summary of the article that « This method can be considered as an improvement of the Ghost-Fluid method, with the specificity of a sharp second-order numerical scheme for the spatial resolution of the discontinuous elliptic problem for the pressure ».

Reviewer 2 Report

This paper presents a numerical method for incompressible flows with large density ratios on cartesian mesh. A sharp resolution was implemented to solve the pressure term across the interface. The proposed method was claimed to have advantages in terms of the utilization in a mono-fluid-Navier-Stokes solver and was compared with the Ghost Fluid and the CSF methods via different test cases. Comparisons show that more stable results are obtained with better mass conservation of each phase.

This is a good contribution to the CFD method community. The manuscript is well structured. This reviewer only has the following minor revision comments:

• The authors should validate the proposed method with some experimental results, as comparisons with other CFD methods and analytic solutions are not enough to justify the accuracy of this method

 

• The authors should improve the following figures as legends and tickers are too small to read: Fig. 9, 10, 11, 13, 14, 15, 16

Comments for author File: Comments.pdf

Author Response

First of all, we want to thank both reviewers for their careful work that helps us to improve the manuscript.

We detail in the following what we have done to answer their remarks

Reviewer 2: 
- « This is a good contribution to the CFD method community. The manuscript is well structured. This reviewer only has the following minor revision comments:
The authors should validate the proposed method with some experimental results, as comparisons with other CFD methods and analytic solutions are not enough to justify the accuracy of this method »

In fact, we already compare our numerical results with experimental data, in the case of the dam break test case. This test case enhances the improved conservativity of the new method which allows to recover the correct front propagation.
There are not, at least to our knowledge, many test cases available  in the literature to perform validations with experimental data in two dimensions. In our bibliography study we found this dam break test case that we presented in the paper, and another test case involving the run-up of a solitary wave (Frantzis and Grigoriadis, J. Comput. Phys. 2019, Vol 376).  This other test case is in fact quite similar to the dam-break test case, excepted that the initial interface is smooth while the initial interface of the dam break is not. 
Moreover, the imparted time to perform the revisions was five days. During these five days we did not have enough time to perform another test case. 

- « The authors should improve the following figures as legends and tickers are too small to read: Fig. 9, 10, 11, 13, 14, 15, 16 »

We increased the size of the figures and changed the legend and ticks to make the figures easier to read.