the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 05 Jul 2022
Spatial filtering in a 6D hybrid-Vlasov scheme for alleviating AMR artifacts: a case study with Vlasiator, versions 5.0, 5.1, 5.2.1
Abstract. Numerical simulation models that are used to investigate the near-Earth space plasma environment require sophisticated methods and algorithms together with high computational power. Vlasiator is a hybrid-Vlasov plasma simulation code that, as of recent technological developments, has been able to perform 6D (3D in ordinary space and 3D in velocity space) simulations using Adaptive Mesh Refinement (AMR). In this work we describe a side effect of using AMR in Vlasiator where the heterologous grid approach creates resolution induced discontinuities due to the different grid resolution levels. The discontinuities cause spurious oscillations in the electromagnetic fields that alter the global results. We present and test a spatial filtering operator for alleviating this artifact without significantly increasing the computational overhead. We demonstrate the operator's use case in large 6D AMR simulations and evaluate its performance with different implementations.
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Status: closed
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RC1: 'Comment on egusphere-2022-420', Anonymous Referee #1, 12 Jul 2022
The manuscript (MS) discusses an important topic – the first application of AMR in Vlasiator with a goal to enable fully 6D simulations. With a few exceptions, the text is well written. The MS, however, needs to be further improved in order to demonstrate the effect of spatial filtering on simulation results in more detail.
Major concerns:
- Fig. 3 and Fig. 8 show numerical artefacts in XY plots but they do not show the AMR mesh. It is not clear how these are related exactly. The MS mentions the AMR mesh can be recovered from these figures (line 143). No, that is not enough. Please show the AMR mesh explicitly.
- Also, why do the authors show smoothed (“fixed”) solutions for Fig.8 but not Fig.3? This is confusing. If you show numerical issues, it makes sense to show how you fix them everywhere.
- What region exactly do those insets in Fig. 8 represent? Why does one show coarse cells and the other shows fine cells while they seem to represent the same AMR mesh with and without filtering?
- What sense does it make to show Fig. 8(d,f) if they cannot be compared to similar unfiltered profiles?
- Given all the above, please show unfiltered and filtered plots side by side for comparison, together with the AMR mesh. Fig 3 and Fig.8(c-f) do not carry much information unless you show their counterparts next to them.
Overall, my major concern is that it is not clear at this point if the authors have “cracked” the problem or not. This spatial filtering may be good enough to regularize the bow shock boundary, but this procedure may result in modifying the global solution considerably. The only way to verify that is to also show a reference solution on a fine uniform mesh. I don’t see those. It looks to me that the MS shows either unfiltered AMR solutions or filtered AMR solutions, without comparing them side by side or showing uniform mesh solutions next to them.
- Lines 39-40: I am actually surprised that Vlasiator uses a semi-Lagrangian scheme in configuration and velocity space. These schemes are known to enhance numerical diffusion due to their inherent need to map Lagrangian particles back to the mesh. Please comment on diffusion effects they cause, compared to high-order Eulerian approaches. I understand that the Lagrangian step preserves positivity and is conservative. However, it is highly diffusive too, which is not discussed here.
Minor Comments:
- Lines 100-105: How is Eq.6 related to numerical filters actually used in the MS? Either strike this equation out or explain how it is supposed to be used. Is ‘j’ the imaginary unit? Is this formula supposed to be used in Fourier transforms? Show that exactly in Eq. 7.
- Line 5: strike out ‘resolution induced’
- Line 14: rephrase with ‘3 dimensions …. space’.
- Line 19: strike out ‘which in practice’
- Line 21: there’s no Gauss law here (divE= 4 pi rho)
- Lines 30-31: Lapenta (2012) is not appropriate for referencing the PIC method in general.
- Line 134: replace ‘artificial step’ by ‘density step’.
Citation: https://doi.org/10.5194/egusphere-2022-420-RC1 -
AC3: 'Reply on RC1', Konstantinos Papadakis, 04 Sep 2022
The authors wish to thank Reviewer #1 for reading our manuscript and
providing useful and constructive comments. Below we list our point-by-point
response to the Reviewer’s comments. Italics are used to list the reviewer’s
comments and our response is in regular font.
Below the authors list the reviewer’s major comments on the manuscript.1. Fig. 3 and Fig. 8 show numerical artefacts in XY plots but they do not
show the AMR mesh. It is not clear how these are related exactly. The MS
mentions the AMR mesh can be recovered from these figures (line 143).
No, that is not enough. Please show the AMR mesh explicitly.We wish to point out that the wording used in Line 143 (“ . . . we demon-
strate results of the boxcar filtering operator in a large magnetospheric
production scale run with four 4 AMR levels as illustrated in Figure 8.”)
is unclear. Figures 8(b,c,e) are quantities on the field solver grid which
is uniform. We have modified the manuscript and now the text reads
(” . . . we demonstrate results of the boxcar filtering operator in a large
magnetospheric production scale run using four AMR levels. Simulation
quantities on the refined AMR mesh are illustrated in Figure 8a and on
the uniform field solver grid in Figures 8(b,c,d).”). To address the raised
point, we have supplemented Figure 1 with an explicit 3D plot of the AMR
Vlasov grid, as the reviewer suggested.2. Also, why do the authors show smoothed (“fixed”) solutions for Fig.8 but
not Fig.3? This is confusing. If you show numerical issues, it makes sense
to show how you fix them everywhere.The aliasing effects on the field-solver quantities illustrated in Figure 3
require a lot of simulation time to propagate into the field solver. The
simulations snapshots in Figure 3 are at t=1096.5 simulation seconds.
Vlasiator is a very computationally expensive code and reproducing the
simulation shown in Figure 3 with the filtering operator active would re-
quire large amounts of computational time, for which we do not currently
have a Tier-0 computational grant. The aliasing results can be qualita-
tively compared between different 3D simulations, as shown in Figures
3(d,f) and Figure 8(d,f). As mentioned in the manuscript it is visible
that the profiles in Figures 8(d,f) are not showing unphysicaloscillations unlike their counterparts in Figures 3(d,f) where the filtering operator is
not used.3. What region exactly do those insets in Fig. 8 represent? Why does one
show coarse cells and the other shows fine cells while they seem to represent
the same AMR mesh with and without filtering?
The spatial coordinates of the insets are exactly the same in Figure 8(a)
and Figure 8(b). Both insets show the mass density at a zoomed in region
close to the Earth’s bow-shock. However, in the revised version of our
manuscript Figure 8(a) illustrates mass density on the AMR Vlasov grid
while Figure 8(b) illustrates mass density on the uniform field solver grid.
The staircase effect is visible at the interfaces of the AMR refinement
levels in Figure 8(a), since the filtering operator is not applied. In Figure
8(b) the filtering operator is applied and the staircase effect is alleviated.
Based on the reviewer’s comment this was not clear enough in the text,
so we have modified the caption of Figure 8 to also read ”. . . The insets
in panels (a,b) show a common zoomed-in region from the bow shock."4. What sense does it make to show Fig. 8(d,f ) if they cannot be compared
to similar unfiltered profiles?
The authors’ goal in showing Fig8(d,f) is to point that with the filter-
ing operator enabled, the quantities on the uniform field-solver grid do
not suffer from the high frequency oscillations that their counterparts in
Fig3(d,f) suffer due to the staircase effect. We think that even though
the two simulations are indeed different, a qualitative comparison of the
electric and magnetic field profiles in Figure 3(d,f) and Figure 8(d,f) is
enough to gauge whether the staircase effect is alleviated or still induces
artifacts in the field solver.5.Given all the above, please show unfiltered and filtered plots side by side
for comparison, together with the AMR mesh. Fig 3 and Fig.8(c-f ) do not
carry much information unless you show their counterparts next to them.
We want to clarify that as mentioned in the manuscript the filtering opera-
tor is only applied to the plasma moments and not to the magnetic/electric
fields. Thus we cannot show what the reviewer asks for since unfiltered
electric/magnetic fields do not exist is a simulation where the filtering op-
erator is active. However, Figure 3 is provided as a point of comparison
between a simulation that does not use the filtering operator and one that
does as illustrated in Figure 8. We have also elected not to show the AMR
mesh as it is too fine to allow for the evaluation of the plot and the mesh
at the same time. In the revised version of the manuscript the zoom-ins
in Figure 8(a,b) have the AMR enabled Vlasov grid overlaid on them as
a point of comparison.6.Overall, my major concern is that it is not clear at this point if the
authors have “cracked” the problem or not. This spatial filtering may be good enough to regularize the bow shock boundary, but this procedure may result in modifying the global solution considerably. The only way to verify
that is to also show a reference solution on a fine uniform mesh. I don’t see those. It looks to me that the MS shows either unfiltered AMR solutions or filtered AMR solutions, without comparing them side by side or showing
uniform mesh solutions next to them.We thank the reviewer for this comment. We agree that the only way
to verify the filtering mechanism would be to compare the filtered re-
sults with a simulation without the filtering which is also artifact-free.
That would mean running a 3D simulation with no AMR, using the
maximum spatial resolution (highest refinement level in the AMR runs
demonstrated in the manuscript) in the whole simulation domain. We
can extrapolate the computational requirements of such a reference so-
lution. Based on the computational resources used for the simulation
in Figure 8, the best case scenario without taking into account scaling
performance, the same simulation with no AMR would require upwards
of 350 MCPUh for a total of 500 simulation seconds. That would make
the simulation about 22 times more expensive than the ones presented
in the manuscript. To put this into perspective, Prace’s EuroHPC JU
Call for Proposals grants at most 306 MCPUh (https://prace-ri.eu/
hpc-access/eurohpc-access/eurohpc-ju-call-for-proposals-for-regular-access-mode/)
on LUMI which ranks 3rd at TOP500 as of June 2022(https://www.
top500.org/lists/top500/2022/06/). Further, the authors wish to point
out that the filtering mechanism is not applied to the highest resolution
regions in the simulation which are the regions with high scientific impor-
tance.Below the authors list the reviewer’s minor comments on the manuscript:
1). Lines 100-105: How is Eq.6 related to numerical filters actually used in
the MS? Either strike this equation out or explain how it is supposed to
be used. Is ‘j’ the imaginary unit? Is this formula supposed to be used in
Fourier transforms? Show that exactly in Eq. 7.
We agree with the reviewer’s comment that this equation is not aiding in
the scientific quality of the manuscript and we have removed it.2. Line 5: strike out ‘resolution induced’
We have removed ”resolution induced” from the text as per the
reviewer’s suggestion.3. Line 14: rephrase with ‘3 dimensions . . . . space’.
Based on the reviewer’s comment this sentence has been modified to:
”. . . hybrid-Vlasov plasma simulation code that models collisionless plasma
by solving the Vlasov-Maxwell system of equations for ion particle distri-
bution functions on a six dimensional Cartesian mesh, representing three
spatial and three velocity dimensions.4. Line 19: strike out ‘which in practice’
Done, thank you.5. Line 21: there’s no Gauss law here (divE= 4 pi rho)
We have modified the text accordingly and thank the reviewer
for pointing this out.6. Lines 30-31: Lapenta (2012) is not appropriate for referencing the PIC
method in general.
We have modified the citation and are now citing Nishikawa et
al. 2021 as more appropriate reference to the Particle-in-Cell method.7. Line 134: replace ‘artificial step’ by ‘density step’.
We have modified the manuscript accordingly.Comment on the Semi-Lagrangian solver
Lines 39-40: I am actually surprised that Vlasiator uses a semi-Lagrangian
scheme in configuration and velocity space. These schemes are known to enhance
numerical diffusion due to their inherent need to map Lagrangian particles back
to the mesh. Please comment on diffusion effects they cause, compared to high-
order Eulerian approaches. I understand that the Lagrangian step preserves
positivity and is conservative. However, it is highly diffusive too, which is not
discussed here.As mentioned in the manuscript Vlasiator uses the SLICE-3D algorithm to
solve the Vlasov equation. Since this is a semi-Lagrangian solver it does not
need to abide by the CFL limit which in essence means that less total steps
are required to propagate the plasma compared to a Eulerian approach. Since
diffusion is accumulated over many simulations steps this aids in keeping the
total diffusion low. Moreover, Vlasiator is using slope limited polynomials for
the mapping instead of tracking Lagrangian quasi-particles and that does not
exactly compare to common SL approaches. Finally, Vlasiator uses a 5th order
polynomial reconstruction to perform the Lagrangian mapping which is accurate
enough to ensure low diffusivity.Citation: https://doi.org/10.5194/egusphere-2022-420-AC3
-
RC2: 'Comment on egusphere-2022-420', Anonymous Referee #2, 14 Aug 2022
This paper designs some kernels to filter the staircase effects arising from AMR, which is innovative. The authors carefully examine the mass conservation and computational overhead. Great work!
We encourage the authors to check WarpX's work (https://warpx.readthedocs.io/en/21.02/theory/amr.html) to see if any techniques related to the absorbing layers can be utilized. Also, moving the codes to the GPU architecture is another trend.
Citation: https://doi.org/10.5194/egusphere-2022-420-RC2 -
AC2: 'Reply on RC2', Konstantinos Papadakis, 31 Aug 2022
This paper designs some kernels to filter the staircase effects arising from
AMR, which is innovative. The authors carefully examine the mass conservation
and computational overhead. Great work!The authors wish to thank the reviewer for his comments on our manuscript.
We encourage the authors to check WarpX’s ( https: // warpx. readthedocs.
io/ en/ 21. 02/ theory/ amr. html work to see if any techniques related to the
absorbing layers can be utilized. Also, moving the codes to the GPU architecture
is another trend.
The authors have modified the introduction to cite WarpX as related work.
However, as also mentioned in the revised version of our manuscript, WarpX’s
methods are not compatible with Vlasiator since Vlasiator does not use a particle
approach to modeling plasmas and also because Vlasiator’s field solver operates
on a uniform mesh.Citation: https://doi.org/10.5194/egusphere-2022-420-AC2
-
AC2: 'Reply on RC2', Konstantinos Papadakis, 31 Aug 2022
-
CEC1: 'Comment on egusphere-2022-420', Juan Antonio Añel, 16 Aug 2022
Dear authors,
Unfortunately, after checking your manuscript, it has come to our attention that it does not comply with our "Code and Data Policy".
https://www.geoscientific-model-development.net/policies/code_and_data_policy.html
In the "Code and Data Availability section" of your manuscript, you state that the code for your work is archived on GitHub. Admittedly, later in the references, a ZENODO repository is cited, as you addressed the previous comments by the Topical Editor. However, the mentioned section must contain this information about the permanent repository. Therefore, please, in a potential reviewed version of your manuscript modify the 'Code and Data Availability' section, including the DOI of the Zenodo repository.Also, I would like to take this opportunity to congratulate you on releasing your code under the GPLv2 license.
Regards,
Juan A. Añel
Geosci. Model Dev. Executive EditorCitation: https://doi.org/10.5194/egusphere-2022-420-CEC1 -
AC1: 'Reply on CEC1', Konstantinos Papadakis, 31 Aug 2022
In the ”Code and Data Availability section” of your manuscript, you state
that the code for your work is archived on GitHub. Admittedly, later in the
references, a ZENODO repository is cited, as you addressed the previous com-
ments by the Topical Editor. However, the mentioned section must contain this
information about the permanent repository. Therefore, please, in a potential
reviewed version of your manuscript modify the ’Code and Data Availability’
section, including the DOI of the Zenodo repository.
We wish to thank the executive editor for reading our manuscript and point-
ing out that our permanent repository is not included in the ’Code and Data
Availability’ section. We have revised that section in our udpate version of the
manuscript to include our Zenodo reference DOI as well.Citation: https://doi.org/10.5194/egusphere-2022-420-AC1
-
AC1: 'Reply on CEC1', Konstantinos Papadakis, 31 Aug 2022
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2022-420', Anonymous Referee #1, 12 Jul 2022
The manuscript (MS) discusses an important topic – the first application of AMR in Vlasiator with a goal to enable fully 6D simulations. With a few exceptions, the text is well written. The MS, however, needs to be further improved in order to demonstrate the effect of spatial filtering on simulation results in more detail.
Major concerns:
- Fig. 3 and Fig. 8 show numerical artefacts in XY plots but they do not show the AMR mesh. It is not clear how these are related exactly. The MS mentions the AMR mesh can be recovered from these figures (line 143). No, that is not enough. Please show the AMR mesh explicitly.
- Also, why do the authors show smoothed (“fixed”) solutions for Fig.8 but not Fig.3? This is confusing. If you show numerical issues, it makes sense to show how you fix them everywhere.
- What region exactly do those insets in Fig. 8 represent? Why does one show coarse cells and the other shows fine cells while they seem to represent the same AMR mesh with and without filtering?
- What sense does it make to show Fig. 8(d,f) if they cannot be compared to similar unfiltered profiles?
- Given all the above, please show unfiltered and filtered plots side by side for comparison, together with the AMR mesh. Fig 3 and Fig.8(c-f) do not carry much information unless you show their counterparts next to them.
Overall, my major concern is that it is not clear at this point if the authors have “cracked” the problem or not. This spatial filtering may be good enough to regularize the bow shock boundary, but this procedure may result in modifying the global solution considerably. The only way to verify that is to also show a reference solution on a fine uniform mesh. I don’t see those. It looks to me that the MS shows either unfiltered AMR solutions or filtered AMR solutions, without comparing them side by side or showing uniform mesh solutions next to them.
- Lines 39-40: I am actually surprised that Vlasiator uses a semi-Lagrangian scheme in configuration and velocity space. These schemes are known to enhance numerical diffusion due to their inherent need to map Lagrangian particles back to the mesh. Please comment on diffusion effects they cause, compared to high-order Eulerian approaches. I understand that the Lagrangian step preserves positivity and is conservative. However, it is highly diffusive too, which is not discussed here.
Minor Comments:
- Lines 100-105: How is Eq.6 related to numerical filters actually used in the MS? Either strike this equation out or explain how it is supposed to be used. Is ‘j’ the imaginary unit? Is this formula supposed to be used in Fourier transforms? Show that exactly in Eq. 7.
- Line 5: strike out ‘resolution induced’
- Line 14: rephrase with ‘3 dimensions …. space’.
- Line 19: strike out ‘which in practice’
- Line 21: there’s no Gauss law here (divE= 4 pi rho)
- Lines 30-31: Lapenta (2012) is not appropriate for referencing the PIC method in general.
- Line 134: replace ‘artificial step’ by ‘density step’.
Citation: https://doi.org/10.5194/egusphere-2022-420-RC1 -
AC3: 'Reply on RC1', Konstantinos Papadakis, 04 Sep 2022
The authors wish to thank Reviewer #1 for reading our manuscript and
providing useful and constructive comments. Below we list our point-by-point
response to the Reviewer’s comments. Italics are used to list the reviewer’s
comments and our response is in regular font.
Below the authors list the reviewer’s major comments on the manuscript.1. Fig. 3 and Fig. 8 show numerical artefacts in XY plots but they do not
show the AMR mesh. It is not clear how these are related exactly. The MS
mentions the AMR mesh can be recovered from these figures (line 143).
No, that is not enough. Please show the AMR mesh explicitly.We wish to point out that the wording used in Line 143 (“ . . . we demon-
strate results of the boxcar filtering operator in a large magnetospheric
production scale run with four 4 AMR levels as illustrated in Figure 8.”)
is unclear. Figures 8(b,c,e) are quantities on the field solver grid which
is uniform. We have modified the manuscript and now the text reads
(” . . . we demonstrate results of the boxcar filtering operator in a large
magnetospheric production scale run using four AMR levels. Simulation
quantities on the refined AMR mesh are illustrated in Figure 8a and on
the uniform field solver grid in Figures 8(b,c,d).”). To address the raised
point, we have supplemented Figure 1 with an explicit 3D plot of the AMR
Vlasov grid, as the reviewer suggested.2. Also, why do the authors show smoothed (“fixed”) solutions for Fig.8 but
not Fig.3? This is confusing. If you show numerical issues, it makes sense
to show how you fix them everywhere.The aliasing effects on the field-solver quantities illustrated in Figure 3
require a lot of simulation time to propagate into the field solver. The
simulations snapshots in Figure 3 are at t=1096.5 simulation seconds.
Vlasiator is a very computationally expensive code and reproducing the
simulation shown in Figure 3 with the filtering operator active would re-
quire large amounts of computational time, for which we do not currently
have a Tier-0 computational grant. The aliasing results can be qualita-
tively compared between different 3D simulations, as shown in Figures
3(d,f) and Figure 8(d,f). As mentioned in the manuscript it is visible
that the profiles in Figures 8(d,f) are not showing unphysicaloscillations unlike their counterparts in Figures 3(d,f) where the filtering operator is
not used.3. What region exactly do those insets in Fig. 8 represent? Why does one
show coarse cells and the other shows fine cells while they seem to represent
the same AMR mesh with and without filtering?
The spatial coordinates of the insets are exactly the same in Figure 8(a)
and Figure 8(b). Both insets show the mass density at a zoomed in region
close to the Earth’s bow-shock. However, in the revised version of our
manuscript Figure 8(a) illustrates mass density on the AMR Vlasov grid
while Figure 8(b) illustrates mass density on the uniform field solver grid.
The staircase effect is visible at the interfaces of the AMR refinement
levels in Figure 8(a), since the filtering operator is not applied. In Figure
8(b) the filtering operator is applied and the staircase effect is alleviated.
Based on the reviewer’s comment this was not clear enough in the text,
so we have modified the caption of Figure 8 to also read ”. . . The insets
in panels (a,b) show a common zoomed-in region from the bow shock."4. What sense does it make to show Fig. 8(d,f ) if they cannot be compared
to similar unfiltered profiles?
The authors’ goal in showing Fig8(d,f) is to point that with the filter-
ing operator enabled, the quantities on the uniform field-solver grid do
not suffer from the high frequency oscillations that their counterparts in
Fig3(d,f) suffer due to the staircase effect. We think that even though
the two simulations are indeed different, a qualitative comparison of the
electric and magnetic field profiles in Figure 3(d,f) and Figure 8(d,f) is
enough to gauge whether the staircase effect is alleviated or still induces
artifacts in the field solver.5.Given all the above, please show unfiltered and filtered plots side by side
for comparison, together with the AMR mesh. Fig 3 and Fig.8(c-f ) do not
carry much information unless you show their counterparts next to them.
We want to clarify that as mentioned in the manuscript the filtering opera-
tor is only applied to the plasma moments and not to the magnetic/electric
fields. Thus we cannot show what the reviewer asks for since unfiltered
electric/magnetic fields do not exist is a simulation where the filtering op-
erator is active. However, Figure 3 is provided as a point of comparison
between a simulation that does not use the filtering operator and one that
does as illustrated in Figure 8. We have also elected not to show the AMR
mesh as it is too fine to allow for the evaluation of the plot and the mesh
at the same time. In the revised version of the manuscript the zoom-ins
in Figure 8(a,b) have the AMR enabled Vlasov grid overlaid on them as
a point of comparison.6.Overall, my major concern is that it is not clear at this point if the
authors have “cracked” the problem or not. This spatial filtering may be good enough to regularize the bow shock boundary, but this procedure may result in modifying the global solution considerably. The only way to verify
that is to also show a reference solution on a fine uniform mesh. I don’t see those. It looks to me that the MS shows either unfiltered AMR solutions or filtered AMR solutions, without comparing them side by side or showing
uniform mesh solutions next to them.We thank the reviewer for this comment. We agree that the only way
to verify the filtering mechanism would be to compare the filtered re-
sults with a simulation without the filtering which is also artifact-free.
That would mean running a 3D simulation with no AMR, using the
maximum spatial resolution (highest refinement level in the AMR runs
demonstrated in the manuscript) in the whole simulation domain. We
can extrapolate the computational requirements of such a reference so-
lution. Based on the computational resources used for the simulation
in Figure 8, the best case scenario without taking into account scaling
performance, the same simulation with no AMR would require upwards
of 350 MCPUh for a total of 500 simulation seconds. That would make
the simulation about 22 times more expensive than the ones presented
in the manuscript. To put this into perspective, Prace’s EuroHPC JU
Call for Proposals grants at most 306 MCPUh (https://prace-ri.eu/
hpc-access/eurohpc-access/eurohpc-ju-call-for-proposals-for-regular-access-mode/)
on LUMI which ranks 3rd at TOP500 as of June 2022(https://www.
top500.org/lists/top500/2022/06/). Further, the authors wish to point
out that the filtering mechanism is not applied to the highest resolution
regions in the simulation which are the regions with high scientific impor-
tance.Below the authors list the reviewer’s minor comments on the manuscript:
1). Lines 100-105: How is Eq.6 related to numerical filters actually used in
the MS? Either strike this equation out or explain how it is supposed to
be used. Is ‘j’ the imaginary unit? Is this formula supposed to be used in
Fourier transforms? Show that exactly in Eq. 7.
We agree with the reviewer’s comment that this equation is not aiding in
the scientific quality of the manuscript and we have removed it.2. Line 5: strike out ‘resolution induced’
We have removed ”resolution induced” from the text as per the
reviewer’s suggestion.3. Line 14: rephrase with ‘3 dimensions . . . . space’.
Based on the reviewer’s comment this sentence has been modified to:
”. . . hybrid-Vlasov plasma simulation code that models collisionless plasma
by solving the Vlasov-Maxwell system of equations for ion particle distri-
bution functions on a six dimensional Cartesian mesh, representing three
spatial and three velocity dimensions.4. Line 19: strike out ‘which in practice’
Done, thank you.5. Line 21: there’s no Gauss law here (divE= 4 pi rho)
We have modified the text accordingly and thank the reviewer
for pointing this out.6. Lines 30-31: Lapenta (2012) is not appropriate for referencing the PIC
method in general.
We have modified the citation and are now citing Nishikawa et
al. 2021 as more appropriate reference to the Particle-in-Cell method.7. Line 134: replace ‘artificial step’ by ‘density step’.
We have modified the manuscript accordingly.Comment on the Semi-Lagrangian solver
Lines 39-40: I am actually surprised that Vlasiator uses a semi-Lagrangian
scheme in configuration and velocity space. These schemes are known to enhance
numerical diffusion due to their inherent need to map Lagrangian particles back
to the mesh. Please comment on diffusion effects they cause, compared to high-
order Eulerian approaches. I understand that the Lagrangian step preserves
positivity and is conservative. However, it is highly diffusive too, which is not
discussed here.As mentioned in the manuscript Vlasiator uses the SLICE-3D algorithm to
solve the Vlasov equation. Since this is a semi-Lagrangian solver it does not
need to abide by the CFL limit which in essence means that less total steps
are required to propagate the plasma compared to a Eulerian approach. Since
diffusion is accumulated over many simulations steps this aids in keeping the
total diffusion low. Moreover, Vlasiator is using slope limited polynomials for
the mapping instead of tracking Lagrangian quasi-particles and that does not
exactly compare to common SL approaches. Finally, Vlasiator uses a 5th order
polynomial reconstruction to perform the Lagrangian mapping which is accurate
enough to ensure low diffusivity.Citation: https://doi.org/10.5194/egusphere-2022-420-AC3
-
RC2: 'Comment on egusphere-2022-420', Anonymous Referee #2, 14 Aug 2022
This paper designs some kernels to filter the staircase effects arising from AMR, which is innovative. The authors carefully examine the mass conservation and computational overhead. Great work!
We encourage the authors to check WarpX's work (https://warpx.readthedocs.io/en/21.02/theory/amr.html) to see if any techniques related to the absorbing layers can be utilized. Also, moving the codes to the GPU architecture is another trend.
Citation: https://doi.org/10.5194/egusphere-2022-420-RC2 -
AC2: 'Reply on RC2', Konstantinos Papadakis, 31 Aug 2022
This paper designs some kernels to filter the staircase effects arising from
AMR, which is innovative. The authors carefully examine the mass conservation
and computational overhead. Great work!The authors wish to thank the reviewer for his comments on our manuscript.
We encourage the authors to check WarpX’s ( https: // warpx. readthedocs.
io/ en/ 21. 02/ theory/ amr. html work to see if any techniques related to the
absorbing layers can be utilized. Also, moving the codes to the GPU architecture
is another trend.
The authors have modified the introduction to cite WarpX as related work.
However, as also mentioned in the revised version of our manuscript, WarpX’s
methods are not compatible with Vlasiator since Vlasiator does not use a particle
approach to modeling plasmas and also because Vlasiator’s field solver operates
on a uniform mesh.Citation: https://doi.org/10.5194/egusphere-2022-420-AC2
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AC2: 'Reply on RC2', Konstantinos Papadakis, 31 Aug 2022
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CEC1: 'Comment on egusphere-2022-420', Juan Antonio Añel, 16 Aug 2022
Dear authors,
Unfortunately, after checking your manuscript, it has come to our attention that it does not comply with our "Code and Data Policy".
https://www.geoscientific-model-development.net/policies/code_and_data_policy.html
In the "Code and Data Availability section" of your manuscript, you state that the code for your work is archived on GitHub. Admittedly, later in the references, a ZENODO repository is cited, as you addressed the previous comments by the Topical Editor. However, the mentioned section must contain this information about the permanent repository. Therefore, please, in a potential reviewed version of your manuscript modify the 'Code and Data Availability' section, including the DOI of the Zenodo repository.Also, I would like to take this opportunity to congratulate you on releasing your code under the GPLv2 license.
Regards,
Juan A. Añel
Geosci. Model Dev. Executive EditorCitation: https://doi.org/10.5194/egusphere-2022-420-CEC1 -
AC1: 'Reply on CEC1', Konstantinos Papadakis, 31 Aug 2022
In the ”Code and Data Availability section” of your manuscript, you state
that the code for your work is archived on GitHub. Admittedly, later in the
references, a ZENODO repository is cited, as you addressed the previous com-
ments by the Topical Editor. However, the mentioned section must contain this
information about the permanent repository. Therefore, please, in a potential
reviewed version of your manuscript modify the ’Code and Data Availability’
section, including the DOI of the Zenodo repository.
We wish to thank the executive editor for reading our manuscript and point-
ing out that our permanent repository is not included in the ’Code and Data
Availability’ section. We have revised that section in our udpate version of the
manuscript to include our Zenodo reference DOI as well.Citation: https://doi.org/10.5194/egusphere-2022-420-AC1
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AC1: 'Reply on CEC1', Konstantinos Papadakis, 31 Aug 2022
Peer review completion
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Konstantinos Papadakis
Yann Pfau-Kempf
Urs Ganse
Markus Battarbee
Markku Alho
Maxime Grandin
Maxime Dubart
Lucile Turc
Hongyang Zhou
Konstantinos Horaites
Ivan Zaitsev
Giulia Cozzani
Maarja Bussov
Evgeny Gordeev
Fasil Tesema
Harriet George
Jonas Suni
Vertti Tarvus
Minna Palmroth
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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