Numerical Solution of the Two-Dimensional Richards Equation Using Alternate Splitting Methods for Dimensional Decomposition
Round 1
Reviewer 1 Report
The paper presents a dimensional splitting algorithm method for solving the 2D Richards
equation. Using the splitting procedure, the solution of the 2D equation is reduced to
the solution of a set of 1D equations in each direction of the coordinate system.
The resulting system of algebraic equations has a tri-diagonal coefficient matrix
which can be solved more efficiently than one of the original 2D case.
They applied this algorithm to a simulation infiltration using an exponential model, for
which an analytical solution is known (Figure 5a). Then, they compare with their numerical results.
I do not understand several points:
I do not see differences between Figures 5b)c)and d). But the Authors mentioned that
there is a difference between the order in applying XZ or ZX due to the effects on the
gravity. This means that the algorithm is not predictable and one has to chose the correct order to get the results. In any case, the numerical simulation is performed in a very small box (Lx=1 m,Lz=2.5m), and thus the algorithm is very limited.
I do not see the advantage of using this algorithm even when the Authors resolve only
a problem where the analytical solution is already known. I think that the idea and the
method is interesting but I would recommend to apply their techniques to a more complex system where the approach and results can be highlighted.
Author Response
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Reviewer 2 Report
The paper authors examine in details the Godunoov method, standard and modified Strang methods at solving 2D Richards equation with splitting procedure. They also propose alternate method that is based on successively reversing the order of integration at each time stage.
The following is a list of my comments for the manuscript:
- For variables in equations 1-4, units should be provided.
- It would be better for interpretation by the reader if the numbers on the y axis in figure 12 were written in scientific format.
- In this article the developed algorithms are tested on very simple two examples. At the end of Conclusions there is an information that the developed splitting method can be used for complex geometries on an irregular grid if a coordinate transformation method is applied. It may be interesed to most readers, a brief description of how this method can be applied to complex practical issues. Such information should appear earlier in the article.
Author Response
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Reviewer 3 Report
See the attached review.
Comments for author File: Comments.pdf
Author Response
Responses attached in separate file
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The Authors have answered all of my questions properly. I recommend this paper for publication, provided the authors mentioned in the conclusions that they use a very small rectangular grid in their numerical simulations.
