Frictionless Motion of Diffuse Interfaces by Sharp Phase-Field Modeling

Round 1

Reviewer 1 Report

This manuscript is a useful addition to the literature on explaining the Sharp Phase-Field Method (SPFM) that was originally proposed by Finel in 2018 (cited as reference 41 in the manuscript). This reviewer has two major concerns: 1) The model was tested on a finite difference framework. What about finite element and finite volume methods? Would the results and conclusions still be valid? 2) Upon checking on reference 50, which was published online prior to submission of manuscript, the reviewer found that a few images in this manuscript look very similar to the ones in reference 50. The authors may want to replace them with entirely new ones. Minor issues such as using capital letters for labellings in figures and minor revisions on english throughout the manuscript is recommended.

Author Response

First of all, we would like to thank the reviewer for careful reading the manuscript. We appreciate here/his valuable comments, which have helped us a lot increasing the readability as well as the overall understandability of the manuscript during the revision. Below, all the comments of the reviewer are repeated in black letters together with our respective reply in blue letters. The changes that have been made in the manuscript during the revision in due to the comments of the reviewers are also market in blue.  

This manuscript is a useful addition to the literature on explaining the Sharp Phase-Field Method (SPFM) that was originally proposed by Finel in 2018 (cited as reference 41 in the manuscript). This reviewer has two major concerns:

1. The model was tested on a finite difference framework. What about finite element and finite volume methods? Would the results and conclusions still be valid? Author reply: First of all, we point out that beside the present finite difference testing the method has already been tested with fast Fourier transformation based solvers, as the original Sharp Phase-Field Method (SPFM) by A. Finel involved a spectral solver. The SPFM involves a strong coupling between the numerical solution method and the imposed modeling potentials. Therefore, we know that the results and conclusions presented here are valid for both methods. We add a paragraph discussing these issues, at the end of section 3.
2. Upon checking on reference 50, which was published online prior to submission of manuscript, the reviewer found that a few images in this manuscript look very similar to the ones in reference 50. The authors may want to replace them with entirely new ones. Author reply: It is true that the figures 3, 5 and 7 are similarly setup than the figures 2, 4 and 5 in reference 50, respectively. This simply relates to the fact that the research work is strongly related. However, the clearly different foci of the two different articles, is also reflected in clear differences between any of the three figure pairs. Figure 2 in reference 50 compares the orientation dependence of the oscillation amplitude for different TI-models, whereas figure 3 in the manuscript manly compares the orientation dependence of the oscillation amplitude for two different profile resolutions. Nevertheless, this figure has been replaced during revision, because of a small plotting error: The labels of the x-axes were missing before, which has been corrected during the revision. Figure 4 in reference 50 contains the calibration factor C R , which is not contained in figure 5 in the manuscript. In turn, figure 5 contains the statement of equal ponderation coefficients for all the TI ⟨ hkl ⟩ -models, which is not given in figure 4 in reference 50. Finally, figure 5 in reference 50 just compares the behavior of just two different models, while also showing the fitted profile width, all based on least square fitting data. In contrast, figure 7 in the manuscript compares the behavior of four different models, based on velocity data that is measured by the newly proposed nonlinear contour interpolation.

Minor issues such as using capital letters for labellings in figures and minor revisions on english throughout the manuscript is recommended. Author reply: The labeling in figures and tables has been consistently changed to lower case letters throughout the manuscript.

Reviewer 2 Report

The article is interesting, written in good scientific language. I consider that the article corresponds to the journal subject and can be published in the form in which it is.

Author Response

Thank you very much for your review.

Reviewer 3 Report

Summary:

The authors created a sharp interface phase field model to reduce the effects of spurious grid friction, grid pinning, and grid anisotropy. They show improvements in each of these areas with the sharp phase field model as compared with a continuum phase field model suggesting that the sharp model may be better for many applications.

Notes:

Page 3 line 77:

Aim of this work is to prove… not proof

Page 5 line 160:

Finite Difference Method spelled wrong

Page 8 line 240:

You define Translational Invariance as TI for the first time here, but TI appears in figure 3 several pages before this with no definition… You then continue to spell out the full words instead of using the abbreviation you just defined.

Major Issues:

I would like to see some sort of analysis comparing computation time and power for the continuum model compared with the sharp model. Are the computing resources required for both the same? Is one much faster than the other? Does the sharper interface model allow for coarser meshing and reduce computing power without sacrificing accuracy? Or does it require as much or more mesh resolution? In Continuum models, thinner interfaces lead to a need for very fine meshes, so it would be good to see some sort of analysis in this area about time and computing power.

Author Response

First of all, we would like to thank the reviewer for careful reading the manuscript. We appreciate her/his valuable comments, which have helped us a lot increasing the readability as well as the overall understandability of the manuscript during the revision. Below, all the comments of each reviewer are repeated in black letters together with our respective reply in blue letters. The changes that have been made in the manuscript during the revision in due to the comments of the reviewers are also market in blue.   Summary: The authors created a sharp interface phase field model to reduce the effects of spurious grid friction, grid pinning, and grid anisotropy. They show improvements in each of these areas with the sharp phase field model as compared with a continuum phase field model suggesting that the sharp model may be better for many applications. Notes:

1. Page 3 line 77: Aim of this work is to prove… not proof Author reply: This error has been corrected
2. Page 5 line 160: Finite Difference Method spelled wrong Author reply: This error has been corrected
3. Page 8 line 240: You define Translational Invariance as TI for the first time here, but TI appears in figure 3 several pages before this with no definition… You then continue to spell out the full words instead of using the abbreviation you just defined. Author reply: For the reason of understandability, we restrict to a minimum number of abbreviations. The remaining ones are basically need as descriptions within the figures, where space limitations do not allow for the full spelling out. Within the manuscript text, we prefer repeated definitions of the abbreviations. The missing definition of the abbreviation TI in the caption of figure 3 as well as in the caption of table 1 has been added. Further, we have increased the consistency in the usage of the abbreviation TI in the revised manuscript.

Major Issues:

1. I would like to see some sort of analysis comparing computation time and power for the continuum model compared with the sharp model. Author reply: We add a discussion on potential computational gains by using the SPFM, at the end of section 3.
2. Are the computing resources required for both the same? Is one much faster than the other? Author reply: At the same numerical resolution, the SPFM involves more calculations on the node level. This higher work load however can be efficiently distributed on parallel computing processors. The advantage of the SPFM comes with the huge savings potential in terms of the number of degrees of freedom required in a phase field simulation.
3. Does the sharper interface model allow for coarser meshing and reduce computing power without sacrificing accuracy? Or does it require as much or more mesh resolution? In Continuum models, thinner interfaces lead to a need for very fine meshes, so it would be good to see some sort of analysis in this area about time and computing power. Author reply: The consequence of true elimination of spurious grid friction and grid pinning is that we obtain higher accuracy at substantially coarser mesh resolution.