Dear Authors,

Thanks for your reply on the referees comments.
Can you send a revised version of the manuscript ?
It will be check again by the referees.

Kind regards,

Marie Dumont

Dear Authors,

Thanks a lot for the work on the new version of the paper.
I feel that now the paper can be published after performing a few more minor revisions.
More specifically,
R#1 : The language around 'guaranteed convergence' is still too imprecise and the personal communications with colleagues should not be a cornerstone of the argument. After fixing these problems, and toning done the language that bashes all other numerical methods, I would be willing to support publication of this paper.

R#2 : Just a last point in the paper, I hope I am not wrong but I still think that revised Eq. 12 does not correspond to the semi-implicit case.
Taking Voller, 1984 equation 3, the semi-implicit case corresponds to theta=0.5 i.e the derivative are centered in space and time. In Eq. 12 the temporal derivative is expressed before the space derivative, so this is the implicit case. (I don't understand the change in the index for conductivity).
I think the authors may just keep their previous version of Eq. 12 and replace the word semi-implicit by implicit.


Thanks a lot,
Best regards,

Marie Dumont

Thanks a lot for taking into account reviewer comments.
I feel that the paper is now ready for publication.

Kind regards,

Marie Dumont