A Simple Line-Element Model for Three-Dimensional Analysis of Steady Free Surface Flow through Porous Media

Round 1

Reviewer 1 Report

aIn their work “A simple line element method for three-dimensional analysis of steady free surface flow through porous media” by Yuan et al., the Authors outline a line element method to avoid the classical finite element method.

My major comments are listed below:

1)     In the introduction (line 44-47) the Authors write that traditional methods (finite element/finite difference method) eliminate the flow contribution in the dry domain. I do not agree: there are software that consider also the flow in the unsaturated zone (for instance, FEMWATER). See also comment 3.

2)     When you use a small Bi (0,1m), in your mathematical concept you assume that Darcy’s law applies also at this small scale; how do you support this assumption?

3)     A positive performance of your method is that it is able to consider the transition zone from saturated conditions to completely dry condition through the lambda l parameter. By my understanding, in an application lambda parameter value has to be defined before computations and its value impacts on the free surface solution: how can the value of lambda be defined before computations?

For sake for information on the existing scientific literature on modelling the unsaturated zone, in order to consider the transition from the saturated zone to the unsaturated zone and related flow, some papers already considered this aspect (e.g. Calamak et al, 2021; Butera et al., 2020). In Butera et al., in particular, Van Genuchten relations were used to describe the physical properties of the unsaturated soil a Matlab post processor code was written to identify the location of the phreatic line at each monitoring section of the levee.

The Authors should recognize that existing literature works have already addressed the role of the unsaturated flow and its impact on the free surface identification and point out the novelty of their work in this context.

4)     In section 4.1 the Authors write that when lambda is less than 0,1 m the solution doesn’t depend on lambda value. I’m not sure that this is a general result because I suppose that it is influenced by the fact that the minimum mesh size used in the experiment is 0,1 m. Please discuss it. Maybe an adimensional parameter  lambda/B would be better for the analysis.

5)     The comparison with literature results is very good, but it does not emerge the superiority of the proposed method considered that commercial softwares are available and it is unthinkable that a professional or a researcher writes his/her codes according your model. Can the Authors explain better the superiority of their model?

6)     In section 4.3 you use B=10m: how do you support this choice of the mesh size?

7)     As it concerns the application to the Kajiwa dam, the presence of the unsaturated zone is evident as the upstream side of the dam is always in contact with water. Which value of lambda was used? Did the tetrahedron element model consider the role of the unsaturated zone.

8)     If I have well understood all the validation cases for comparison consider other methods that don’t take into account the role of the unsaturated zone. Hence, how can you check the performance of your method and its ability in modeling the transition from the dry to the wet zone?

So, my comments to the Authors address mainly the test on their lambda parameter, that is modelling the unsaturated zone. If they clarify this point, the quality of the manuscript increases. 

 

 

Minor comments:

The velocity symbol in eq.1 ad 2 are different from those of the text.

Pressure head is usually p/g

Formula (29): explain R

Caption of Figure 3: (b) it is not clear the method used for the computation of water head distribution

Formula at lines 221 are not on the text line

Figures 8 and 9: the reference axis should be inserted.

Line 280 typo: behavior not bahavior

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

The authors have formulated the FEM simulations of the problem in the title of the paper using an unconventional approach away from the continuum hypothesis in fluid mechanics by considering the flow through a porous media. The numerical method is designed  accordingly to capture the flow through the pores (three dimensional network of line elements) only.  The working machinery developed is interesting and so do the numerical results. The numerical method developed in the paper under review is claimed to be equivalent to the other conventional methods, but the present method is more realistic from physical point of view. In my view, the work is interesting and is acceptable for publication in Water.

However, the Appendix is too short and so, the authors should remove the appendix and insert the underlying text where the text belongs to.

 

 

   

Author Response

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Author Response File: Author Response.docx