An Adaptive Degree of Freedom Condensation Algorithm for Simulating Transient Temperature, Applied to an Asphalt-Concrete Core Wall

Round 1

Reviewer 1 Report

1. What is the aim of such simulation itself: to find precisely max. temperatures (so the initial part is important) or to determine the time when the temperature in the specimen is lower than prescribed threshold (to safely add a next layer) or …?  One may think the second guest is correct. If it so, the next question appears: what is the influence of the mesh on the results at the “end” of the simulation time? To we really need refined FE-meshes?

2.  I'm not sure it is the best approach to use terms 'stiffness matrix' and 'force vector' in heat transfer analysis (Section 2)

3. “If a node corresponds to multiple DOFs such as displacement in multiple directions” – what does it mean in a context of temperature?

4. How  ADOF-FEM method is implemented?

5. The issue of the bandwidth increase of the "stiffness matrix' is not discussed.

6. The example 1 does not fit into the core of the paper (steel is simulated). Why steel? The difference between the initial temperature and outside temperature is very large, not applicable when analysing the concrete asphalt structures. The same remark applies to the time increment.

7.  I'm not sure the comparison of different errors smaller generally than 1% can provide clear and always correct trends (See Example 1).

8. The choice of the simulation end greatly influences the obtained time savings. How it is assumed in all examples? Please notice the number of DOF in Example 1 remains unchanged from the half of the simulation time, while in Example 2 it decreasing during the whole calculation (it is not constant).

9. Example 1 - the time reduction is not very impressive. I suspect the time benefit would be even smaller if the simulations would stop at approx. 2000 seconds (see Figure 3).

10.   Why you don't compare results with analytical solution in Table 2?

11.   What is the maximum temperature change starting from 66h (Figs. 8 and 9) till the end? What error can we obtain if the simulations stops after 66 h (not after 160 h)?

12.   Example 3 – can you scale geometry without not scaling material constants? How to interpret results? Besides layer thickness is not scaled there, although in the Introduction it was mentioned it is an important issue (layer thickness with respect to specimen dimensions).

13.   Tolerance values are not given while they influences strongly the mesh adaptation process.

14.   Small errors:

a.       line 6: is constructed base on the shape -> is constructed based on the shape

b.       line 8: identify the positions whose -> identify the positions where

c.       line 39: there are few research -> there are few research studies

d.       Table 1 - time unit is missing

e.       line 372: As can be seen from Table 1, -> As can be seen from Table 2,

f.        line 436: in the Figur 5. -> in the Figure 5.

g.       line 449: The positions with large temperature -> The points with ...

 

Author Response

We would like to thank you for your careful reading, helpful comments, and constructive suggestions, which has significantly improved the presentation of our manuscript.

We have carefully considered all comments from the reviewers and revised our manuscript accordingly. The manuscript has also been double-checked, and the typos and grammar errors we found have been corrected. In the attachment, we summarize our responses to each comment from the reviewers. We believe that our responses have well addressed all concerns from the reviewers. We hope our revised manuscript can be accepted for publication.

Author Response File: Author Response.docx

Reviewer 2 Report

A novel adaptive degree of freedom condensation algorithm for simulating transient temperature is proposed to solve the problem of huge cost of transient temperature simulation in the whole construction process of asphalt concrete core wall. The paper is well written and can be accepted for publication upon some minor spell checks, e.g., ln 6, ‘base’ should be ‘based’.

Author Response

We would like to thank you for your careful reading and positive comments on our research. The spelling problem you mentioned has been corrected in the new version of the manuscript.

Reviewer 3 Report

In this paper, the algorithm named ADOF-FEM and the corresponding coarsening judgment criterion was presented to solve the problem of the huge computational cost of the asphalt concrete core wall transient temperature simulation during the construction period. And, validate of the presented method was verified with two numerical examples. There are some issues should be solved before publication.

1. No further explanation for the effect of core wall temperature on the impermeability of the core wall.

2. Table 1 data correspondence is not clear enough, suggest to modify the format.

3. Example 2 is better if there is a scale down experiment to compare.

4. The model in example 2 has only 4 layers of asphalt concrete, whether the number of layers is too small will have an impact on the cooling of each layer of concrete, and whether the impact will have a greater impact on the accuracy of the simulation.

5. Is it more reasonable to set the outer lateral boundary of the example as the heat sink boundary?

6. The 1:10 scale model used in Example 3, if a larger model is used for the simulation, will it have an impact on the accuracy.

7. Figure 13 of example 3, suggests to put the normal mesh finite element calculation results also to form a comparison.

8. The computational cost saved by ADOF-FEM is mainly the two parts of matrix factorization and solving equation in FEM. Is there an upper limit in using ADOF-FEM to save the computational cost?

9. A total of 40 references, 19 of which are more than 10 years old.

10. What is the compression criterion for the node degrees of freedom of the mesh?

11. The article illustrates that the temperature of the external rock pile has a small effect on the core wall, but the effect of other factors on the temperature of the core wall has not been studied; would it be better to add such studies.

Author Response

We would like to thank you for your careful reading, helpful comments, and constructive suggestions, which has significantly improved the presentation of our manuscript.

We have carefully considered all comments from the reviewers and revised our manuscript accordingly. The manuscript has also been double-checked, and the typos and grammar errors we found have been corrected. In the attachment, we summarize our responses to each comment from the reviewers. We believe that our responses have well addressed all concerns from the reviewers. We hope our revised manuscript can be accepted for publication.

Author Response File: Author Response.docx

Round 2

Reviewer 3 Report

This paper can be accept in present form.