Comparison of the Performance of New and Traditional Numerical Methods for Long-Term Simulations of Heat Transfer in Walls with Thermal Bridges
Round 1
Reviewer 1 Report
The manuscript presents a very hard work made by the Authors. It is very interesting to compare the existing methods with a new one. Authors developped their own methods and describe them in details in this paper. I miss more critical comparison with the Ansys and Matlab. Several times you are using the word 'best method'. I miss the answer - why best? There are no universal best numerical methods. Every method has its weaks. I need more critical point of view.
Do you plan to simulate also other kind of thermal bridges? Is your method adequate to calculate temperature distribution in the areas adjacent to air leaks in building elements? I would appreciate your comments in conclusion.
Author Response
“The manuscript presents a very hard work made by the Authors. It is very interesting to compare the existing methods with a new one. Authors developped their own methods and describe them in details in this paper. I miss more critical comparison with the Ansys and Matlab. Several times you are using the word 'best method'. I miss the answer - why best? There are no universal best numerical methods. Every method has its weaks. I need more critical point of view.”
Answer: We state that these are the best methods only for that specific problem (heat transfer in a wall). We do not and cannot state that they are generally the best. They have weaknesses, of course: The Dufort-Frankel is a two-step method, so it is hard to develop an adaptive time step version of it. On the other hand, the LH needs a special odd-even mesh, so it cannot be applied easily for all geometry. However, in terms of accuracy vs running time, they were clearly the best (with sometimes the OOEH), which was demonstrated in our previous papers as well, where they were compared to several other methods.
But, for example, we haven’t tried to apply them to solve Navier-Stokes equation to accurately simulate the motion of air around building components.
“I miss more critical comparisons with the Ansys and Matlab”
Answer: MATLAB is a general-purpose mathematical software, while Ansys is a simulation software. The respected reviewer probably means that we should compare Ansys with our codes written in MATLAB. We have now inserted the following paragraph to react to this comment:
Nevertheless, we absolutely do not intend to suggest that ANSYS and similar solvers are redundant since there are faster numerical algorithms than those they employ. These simulation software automatically generate the mesh and present graphically the results, while if someone chooses to write an own code, these are tedious work, especially in the case of complicated geometries. Moreover, the explicit and stable methods haven’t been applied to cases involving the simulation of the motion of the air, e.g. for the problem of air leakage in building components, while the simulation software routinely handles these problems. However, we think that in the already well-established cases, such as those types studied in this paper, the simulation software could incorporate the proposed algorithms as an option can be chosen by the users or by an artificial intelligence.
“Do you plan to simulate also other kind of thermal bridges?”
Answer: Yes, we do. In the conclusion section we wrote that we want to study the real thermal bridges in blocks of flats. For this purpose, we are now developing the 3D version of our code.
“Is your method adequate to calculate temperature distribution in the areas adjacent to air leaks in building elements?”
Answer: Since the mentioned problem contains the modelling of the motion of the air, currently the research is not at the stage we could answer this question by yes or no. The new paragraph above mentions a few lines about this problem as well. However, we are especially grateful for this question from the point of view of our future research.
Reviewer 2 Report
Authors of the article test a simulation methodology based on fundamental physical principles to asses heat transfer in the walls with thermal bridges.
The present paper is interesting. The chosen method for this research is adequately described. The description of the research is clear. However, the study needs to consider additional literature review to highlight importance of this research. It is noted that almost 20% are own publications.
Author Response
“However, the study needs to consider additional literature review to highlight importance of this research. It is noted that almost 20% are own publications.”
Answer: We have now extended our literature review and added 6 extra references (none of them are self-citations) and 3 ISO Standards.
Reviewer 3 Report
In this paper, different numerical methods are used to solve the heat transfer problem of building walls. By comparing the performance of other solvers, the two best methods are selected and used to simulate the two-dimensional space system for a long time. This topic is valuable, and can provide reference for the application of thermal Bridges with different shapes in buildings, so as to improve energy efficiency. Whereas, the following comments should be properly addressed before it is accepted:
1. The word of the formula is suggested to be adjusted to Times New Roman. In addition, there are some small details that need to be noted. When subscript is not a variable, it should be positive. For example, Qcell subscript should be positive.
2. The table is recommended to be a three-line table.
3. The two best approaches described in sections 4.3 and 5.1 are different.
4. Figure 7 shows the maximum errors as a function of the running time for the tested methods in the case of the medium mesh. Why is it stated in line 475 that the accuracy of methods increases as the resolution of the mesh increases?
5. It is suggested that the author change all the legends in the paper to have no filling color and no border, because the white background will block the information in the picture.
6. It is suggested that the author should adjust the upper and lower limits of the scales in the paper to ensure the complete display of the graph information.
7. Introduction: the topic of this study is to improve the energy efficiency, thus the description about energy saving should be added. The author can read and cite the paper: Environmental and economical analyses of transcritical CO2 heat pump combined with direct dedicated mechanical subcooling (DMS) for space heating in China. Energy Conversion and Management, 2019, 198: 111317, which can improve the quality of this paper.
8. The novelty of this study should be enhanced.
Author Response
“The word of the formula is suggested to be adjusted to Times New Roman.”
Answer: We used the template of the journal, and if the editor requires us to change the font type, we will change that.
“In addition, there are some small details that need to be noted. When subscript is not a variable, it should be positive. For example, Qcell subscript should be positive.”
Answer: We don’t know what the reviewer means ‘positive’ in this context, but the reviewer is right that in some cases, these subscripts were italics. We have now changed these words in all subscripts in the equations to non-italic form.
“The table is recommended to be a three-line table.”
Answer: We have now modified all the tables accordingly.
“The two best approaches described in sections 4.3 and 5.1 are different.”
Answer: We agree with the reviewer that in 4.3 our statements were not completely clear. Now we have modified this sentence as follows: ”The leapfrog-hopscotch with the pseudo-implicit treatment (LH-PseudpImp) of the radiation term and the Dufort-Frankel schemes with the pseudo-implicit treatment of both the convection and the radiation term (DF-D) are the two best methods.”
“Figure 7 shows the maximum errors as a function of the running time for the tested methods in the case of the medium mesh. Why is it stated in line 475 that the accuracy of methods increases as the resolution of the mesh increases?”
Answer: We removed this sentence from the revised version. Although it is true that the accuracy is increasing with the refinement of the (spatial) mesh, since we use a MATLAB ode solver as a reference, which already contains the error of space discretization, this improvement is not visible in the figures. We modified a sentence in p. 17 in a similar way: “We notice that the accuracy of the ANSYS solvers is positively affected by the smoothing of the mesh, the errors are decreasing with the time step size.”
“It is suggested that the author change all the legends in the paper to have no filling color and no border, because the white background will block the information in the picture.”
Answer: We have checked, and all the legends’ background is colorless. We use the default setting in MATLAB and in all our previous publications it was accepted.
“It is suggested that the author should adjust the upper and lower limits of the scales in the paper to ensure the complete display of the graph information.”
Answer: we think that all the information is properly displayed. The limits of the scales are required to be the same on the left and right sides of e. g. Fig. 14. for comparability.
“Introduction: the topic of this study is to improve the energy efficiency, thus the description about energy saving should be added. The author can read and cite the paper: Environmental and economical analyses of transcritical CO2 heat pump combined with direct dedicated mechanical subcooling (DMS) for space heating in China. Energy Conversion and Management, 2019, 198: 111317, which can improve the quality of this paper.”
Answer: We are grateful to the reviewer for suggesting us this very relevant paper. We have read and cited that paper among some others to extend our introduction.
“The novelty of this study should be enhanced.”
Answer: Now we have made an attempt to further clarify the novelty of our paper as the editor also suggested.
