Non-Hydrostatic Discontinuous/Continuous Galerkin Model for Wave Propagation, Breaking and Runup
Round 1
Reviewer 1 Report
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Comments for author File: 
Comments.pdf
Author Response
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Reviewer 2 Report
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Comments for author File: Comments.pdf
Author Response
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Reviewer 3 Report
GENERAL COMMENTS
This manuscript proposes a two-dimensional depth-integrated non-hydrostatic model using a combination of continuous and discontinuous Galerkin methods. The momentum equations without the non-hydrostatic pressure terms are solved by a discontinuous Galerkin method. The non-hydrostatic pressure is computed by a continuous Galerkin method using quadrilateral finite elements.
In order to remove high-frequency spurious oscillations that appear using discontinuous Galerkin methods, and also to maintain the necessary accuracy in smooth regions, a new slope limiter for discontinuous quadrilateral elements is proposed.
Overall, this study places the context of the analysis well. The introduction is sufficiently substantiated, the mathematical formalisms are clear and the discussions and conclusions are generally consistent with the comparisons of numerical results with an analytical solution and five sets of laboratory experiments.
However, several statements are not completely understandable and further explanations are required. Examples are, among others: lines 96-97 (series of analytical solutions of what?); line 133 (and what about the shallow water conditions? Clarify); line 257 (clarify); line 389 (clarify); lines 396-397 (which "corresponding analytical formula"? Clarify); lines 637-643 (what about the surface variation criterion? "Excellent similarities"? A more explanatory discussion, including the wave breaking process, is needed); lines 642-643 (clarify),...
In some sets, the statements made about the quality of the numerical results are not entirely correct; more care and correction are recommended. Less favorable results should also be discussed in more detail (why and how to improve).
The wave breaking criterion seems to anticipate the reduction in wave amplitude (Figures 8 and 9), i.e., it appears to be too (or too quickly) dissipative; can't the process be improved?
The system of equations (45)-(46) is not a solution of equations (1)-(4), assuming the linear distribution of the non-hydrostatic pressure in the vertical direction. Although the numerical results may be considered acceptable for A/h = 0.2 (figures 3 and 4), higher values of the relationship A/h should be discussed, up to about 0.5.
Example 3.6, Figure 15 shows notable differences in gauges G3 and G6; sufficiently convincing explanatory material is expected. In this case, there also seems to be a mismatch at the beginning of the breaking process (in both Figures 15 and 16).
Velocity fields (vector fields) at representative times would be useful in both simulations 3.5 and 3.6 (one instant sufficiently representative in each of the experiments).
Looking to be constructive, in addition to the General Comments above, I would like to point out the following Specific Remarks.
SPECIFIC REMARKS
- Check equation (41) (second term of the right hand).
- The sequence of numerical operations (flowchart) would help.
- What is D in Table 1 (will not be h)?
- What wave breaking criterion was used in the simulations of sets 3.2, 3.3, 3.5, and 3.6?
- Several Figure captions are very telegraphic and should be more explanatory of the Figure contents, especially Figure 2 caption (distinguish it from Figure 1 caption), Figure 3 caption (should include the water depth, wave height, grid, and time step), Figure 4 caption (should include the water depth, wave height, and time steps), Figure 5 caption (should include the still water depth, wave height, grid, and time step), Figure 6 caption (should include the still water depth, wave height, grid, and time step), captions of Figures 8 and 9 (should include the still water depth, wave height, grid, and time step), Figure 12 caption (should include the grid, and time step), Figure 14 caption (should include the still water depth, wave height, and grid), captions of Figures 15 and 16 (should include the still water depth, wave height, grid, and time step).
Author Response
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Reviewer 4 Report
The Authors present a depth-averaged, non-hydrostatic numerical model for simulation of wave propagation, breaking and run-up, using a combination of continuous and discontinuous Galerkin methods. Special focus is given on the development of a slope limiter for quadrilateral elements, which is presented in detail. Finally, the numerical model is validated, compared with analytical solutions and a number of experimental measurements.
The manuscript is quite interesting and it is very well written. The numerical methods are presented in detail and the numerical results are quite comprehensible and in agreement with the analytical solutions and the experimental measurements. I have noticed only some minor deficiencies which should be addressed in order to improve the quality of the manuscript.
My opinion is that that the manuscript can be accepted for publication if the Authors address the comments in the attached pdf file.
Comments for author File: Comments.pdf
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Dear authors,
In spite of your efforts made for aligning the style of the paper with the recommendations of the reviewers, there are some minor corrections that are still necessary. Concretely:
Please check carefully the style of the equations, i.e. some of them are typed in bolt, some other not;
Fig. 8 still shows some unwanted characters on its left margin. Please remove them;
Fig. 13: Circles seem to be deformed. Please check and eventually redraw.
Author Response
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