От: Shkvar Eugene
Комментарий: Incredibly complex statement of a solved problem leaves a fantastically positive impression. Thank you so much for this pleasure. Nevertheless, it is interesting to ask the respected authors of this research about their point of view regarding the following problem: they have applied an upwind finite difference scheme for the convective terms of governing equations for fluid-dynamical part of the problem, so the order of accuracy of the corresponding finite-difference approximation in space is only the first. On the other side, they must solve these equations a lot of times due to negligibly small step in time, that is connected with necessity of plasma dynamics simulation. So the first question, initiated by these circumstances, is about kind of finite-difference approximation in time, applied in frames of this investigation (explicit or implicit). According to this let me formulate several related questions. Did you use some special methods to achieve a stability of a computational process in time? Can you estimate quantitatively the role and negative influence of errors due to the first order of approximation in space on the final numerical data, obtained as a result of integrating the fluid-dynamical equations with applied so small step in time? And what will happen in case of generalization of this problem formulation from 1D to 2D o3 3D cases? Thank you in advance for your attention to my position and corresponding questions regarding this actual research.
От: Albina Tropina
Ответ на комментарий: Thank you very much for attention to my work. I will try to answer all the questions. Yes, the first version of the code was with the upwind scheme of the first order in time, just now we have MUSCL-Hancock scheme of the second order accuracy so the problem of accuracy has already improved.
We use explicit formulation and did not use any special methods to achieve a stability of a computational process in time.
The calculation process was organized as follows: fluid is supposed to be frozen when electrons and ions are migrating in the electric field so one step in time for fluid-dynamic equations (NS) corresponds to 10^3-10^4 steps in time for other processes. We are going to implement the same problem formulation for 2D case, but
we haven't figured out yet all the details in this case. Thank you very much again for your attention to our work.
От: Igor Selezov
Ответ на комментарий:
I thank Prof. Eugene Shkvar for your comments related to a computer simulation mainly of such complicated phnomena in a plasma. Nevertheless, the possibilities to construct some analytical models are of a great interest and should be considered as well.