Dear Lammps users,
I have been quite reluctant to post this problem on the Lammps email list as it could be considered one which relates more to theory than a Lammps methodology.
I have been performing non-equilibrium simulations of homogenous systems of varying complexity using the “fix heat” command to create a one dimensional non-linear temperature gradient. I then analyze the numerical derivative of the temperature profile in the dimension of the applied heat flux to calculate a “local” thermal conductivity. The temperature gradients produced are non-linear and typically vary by a factor of two over the simulated area. I have done a comparison of these NEMD results with simulations a colleague has ran using GROMACS with small linear linear gradients and the agreement is to within around 1%.
It is my feeling therefore that these NEMD simulations are acceptably accurate.
It was however my initial intention to try and prove the validity of this non-linear temperature gradient technique by performing separate NVE Green-Kubo calculations using the local density and temperature at given points along my NEMD simulations.
The comparison of both the non-linear temperature gradient method and GK method for calculation of the thermal conductivity show very good agreement for two initial systems, namely a pure Lennard-Jones system and a harmonic dumbbell system. The comparison for my latest system (SPC/E water using pppm for the electrostatics) however differs by quite a large factor (~14%). I particular it appears to systematically be higher for the Green-Kubo calculations.
Unfortunately after a significant search I have not been able to find any direct comparisons of the thermal conductivity for SPC/E water by Green-Kubo and NEMD, however there are papers which show good agreement for the viscosity.
I guess simply put, my question is:
Have there been any bench mark tests performed for the stress-tensor/viral K-space components (In particular using pppm)?
Many thanks and apologies for the non-specific nature of the question, Jeff.
Hi Jeff,
Here are my two cents. While I haven’t done any bench marking as you requested. I have performed some simulations (~4 years back) for epoxies with Green-Kubo and NEMD methods. For Green-Kubo, I used ewald (had my own code at that time which included portions of ewald.cpp of lammps; Green-kubo formalism was not incorporated in lammps at that time) as I could understand that better. I also saw about 20% higher thermal conductivity in Green-Kubo approach. I did not try PPPM at that time as I could not understand workings of PPPM to the detail I wanted to. Ewald was on the other hand was much more straightforward and there was some literature explaining the equations.
I hope this help. If you are interested, you can look at Varshney et al. Polymer, 2009, 50, 3378.
Best Regards,
Vikas
You could try measuring kappa for rigid and flexible water. I think
there are SPC/E variants that allow for flexible bonds. It's possible
that the constraints enforced by SHAKE affect kappa.
Steve
Hi Jeff,
We recently completed a project to compare water models using NEMD and GK methods. We see good agreement with LAMMPS using both of the ‘per-atom’ k-space methods (Ewald and PPPM) and with NEMD. As Steve pointed out, the constraints change the TC. There is a recent paper with a good discussion from the group of Muller-Plathe. I also recommend Vikas’ paper (below), it has a nice breakdown of the different contributions to TC.
Tim
Thank you for all the replies. I am actually in the middle of carrying out some simulations that I was hoping would provide a good test of the K-space contributions to the virial.
As a first test I have tried to reproduce a Green-Kubo based thermal conductivity calculation from the paper "J. Chem. Phys. 120, 8676 (2004)".
I ran the simulations for approximately the same system conditions ~256 atoms T=1339K D=1.433 g/cm^{3}and the same duration/sampling but get a thermal conductivity which is ~40% larger.
As a secondary test I have started running an NEMD calculation with the same system to see whether the results agree with either the Lammps' Green-Kubo calculations or those of the aforementioned paper in view validating either.
It is good to hear though that you found agreement for water using both NEMD and Green-Kubo. Would it be possible for you to give me an approximate figure for the % agreement you get between both methods and at what temperature and density the simulations were performed.
I have attached an eps image showing the comparison I mentioned earlier for NaCl
Many thanks, Jeff.
lammps_test.eps (28.7 KB)