forked from lijiext/lammps
188 lines
6.8 KiB
Plaintext
188 lines
6.8 KiB
Plaintext
"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
|
|
|
|
:link(lws,http://lammps.sandia.gov)
|
|
:link(ld,Manual.html)
|
|
:link(lc,Section_commands.html#comm)
|
|
|
|
:line
|
|
|
|
compute heat/flux command :h3
|
|
|
|
[Syntax:]
|
|
|
|
compute ID group-ID heat/flux ke-ID pe-ID stress-ID :pre
|
|
|
|
ID, group-ID are documented in "compute"_compute.html command
|
|
heat/flux = style name of this compute command
|
|
ke-ID = ID of a compute that calculates per-atom kinetic energy
|
|
pe-ID = ID of a compute that calculates per-atom potential energy
|
|
stress-ID = ID of a compute that calculates per-atom stress :ul
|
|
|
|
[Examples:]
|
|
|
|
compute myFlux all heat/flux myKE myPE myStress :pre
|
|
|
|
[Description:]
|
|
|
|
Define a computation that calculates the heat flux vector based on
|
|
contributions from atoms in the specified group. This can be used by
|
|
itself to measure the heat flux into or out of a reservoir of atoms,
|
|
or to calculate a thermal conductivity using the Green-Kubo formalism.
|
|
|
|
See the "fix thermal/conductivity"_fix_thermal_conductivity.html
|
|
command for details on how to compute thermal conductivity in an
|
|
alternate way, via the Muller-Plathe method. See the "fix
|
|
heat"_fix_heat.html command for a way to control the heat added or
|
|
subtracted to a group of atoms.
|
|
|
|
The compute takes three arguments which are IDs of other
|
|
"computes"_compute.html. One calculates per-atom kinetic energy
|
|
({ke-ID}), one calculates per-atom potential energy ({pe-ID)}, and the
|
|
third calcualtes per-atom stress ({stress-ID}). These should be
|
|
defined for the same group used by compute heat/flux, though LAMMPS
|
|
does not check for this.
|
|
|
|
The Green-Kubo formulas relate the ensemble average of the
|
|
auto-correlation of the heat flux J to the thermal conductivity kappa:
|
|
|
|
:c,image(Eqs/heat_flux_J.jpg)
|
|
|
|
:c,image(Eqs/heat_flux_k.jpg)
|
|
|
|
Ei in the first term of the equation for J is the per-atom energy
|
|
(potential and kinetic). This is calculated by the computes {ke-ID}
|
|
and {pe-ID}. Si in the second term of the equation for J is the
|
|
per-atom stress tensor calculated by the compute {stress-ID}. The
|
|
tensor multiplies Vi as a 3x3 matrix-vector multiply to yield a
|
|
vector. Note that as discussed below, the 1/V scaling factor in the
|
|
equation for J is NOT included in the calculation performed by this
|
|
compute; you need to add it for a volume appropriate to the atoms
|
|
included in the calculation.
|
|
|
|
IMPORTANT NOTE: The "compute pe/atom"_compute_pe_atom.html and
|
|
"compute stress/atom"_compute_stress_atom.html commands have options
|
|
for which terms to include in their calculation (pair, bond, etc).
|
|
The heat flux calculation will thus include exactly the same terms.
|
|
Normally you should use "compute stress/atom
|
|
virial"_compute_stress_atom.html so as not to include a kinetic energy
|
|
term in the heat flux.
|
|
|
|
This compute calculates 6 quantities and stores them in a 6-component
|
|
vector. The first 3 components are the x, y, z components of the full
|
|
heat flux vector, i.e. (Jx, Jy, Jz). The next 3 components are the x,
|
|
y, z components of just the convective portion of the flux, i.e. the
|
|
first term in the equation for J above.
|
|
|
|
:line
|
|
|
|
The heat flux can be output every so many timesteps (e.g. via the
|
|
"thermo_style custom"_thermo_style.html command). Then as a
|
|
post-processing operation, an autocorrelation can be performed, its
|
|
integral estimated, and the Green-Kubo formula above evaluated.
|
|
|
|
The "fix ave/correlate"_fix_ave_correlate.html command can calclate
|
|
the autocorrelation. The trap() function in the
|
|
"variable"_variable.html command can calculate the integral.
|
|
|
|
An example LAMMPS input script for solid Ar is appended below. The
|
|
result should be: average conductivity ~0.29 in W/mK.
|
|
|
|
:line
|
|
|
|
[Output info:]
|
|
|
|
This compute calculates a global vector of length 6 (total heat flux
|
|
vector, followed by conductive heat flux vector), which can be
|
|
accessed by indices 1-6. These values can be used by any command that
|
|
uses global vector values from a compute as input. See "this
|
|
section"_Section_howto.html#howto_15 for an overview of LAMMPS output
|
|
options.
|
|
|
|
The vector values calculated by this compute are "extensive", meaning
|
|
they scale with the number of atoms in the simulation. They can be
|
|
divided by the appropriate volume to get a flux, which would then be
|
|
an "intensive" value, meaning independent of the number of atoms in
|
|
the simulation. Note that if the compute is "all", then the
|
|
appropriate volume to divide by is the simulation box volume.
|
|
However, if a sub-group is used, it should be the volume containing
|
|
those atoms.
|
|
|
|
The vector values will be in energy*velocity "units"_units.html. Once
|
|
divided by a volume the units will be that of flux, namely
|
|
energy/area/time "units"_units.html
|
|
|
|
[Restrictions:] none
|
|
|
|
[Related commands:]
|
|
|
|
"fix thermal/conductivity"_fix_thermal_conductivity.html,
|
|
"fix ave/correlate"_fix_ave_correlate.html,
|
|
"variable"_variable.html
|
|
|
|
[Default:] none
|
|
|
|
:line
|
|
|
|
# Sample LAMMPS input script for thermal conductivity of solid Ar :pre
|
|
|
|
units real
|
|
variable T equal 70
|
|
variable V equal vol
|
|
variable dt equal 4.0
|
|
variable p equal 200 # correlation length
|
|
variable s equal 10 # sample interval
|
|
variable d equal $p*$s # dump interval :pre
|
|
|
|
# convert from LAMMPS real units to SI :pre
|
|
|
|
variable kB equal 1.3806504e-23 # \[J/K\] Boltzmann
|
|
variable kCal2J equal 4186.0/6.02214e23
|
|
variable A2m equal 1.0e-10
|
|
variable fs2s equal 1.0e-15
|
|
variable convert equal $\{kCal2J\}*$\{kCal2J\}/$\{fs2s\}/$\{A2m\} :pre
|
|
|
|
# setup problem :pre
|
|
|
|
dimension 3
|
|
boundary p p p
|
|
lattice fcc 5.376 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
|
|
region box block 0 4 0 4 0 4
|
|
create_box 1 box
|
|
create_atoms 1 box
|
|
mass 1 39.948
|
|
pair_style lj/cut 13.0
|
|
pair_coeff * * 0.2381 3.405
|
|
timestep $\{dt\}
|
|
thermo $d :pre
|
|
|
|
# equilibration and thermalization :pre
|
|
|
|
velocity all create $T 102486 mom yes rot yes dist gaussian
|
|
fix NVT all nvt temp $T $T 10 drag 0.2
|
|
run 8000 :pre
|
|
|
|
# thermal conductivity calculation, switch to NVE if desired :pre
|
|
|
|
#unfix NVT
|
|
#fix NVE all nve :pre
|
|
|
|
reset_timestep 0
|
|
compute myKE all ke/atom
|
|
compute myPE all pe/atom
|
|
compute myStress all stress/atom virial
|
|
compute flux all heat/flux myKE myPE myStress
|
|
variable Jx equal c_flux\[1\]/vol
|
|
variable Jy equal c_flux\[2\]/vol
|
|
variable Jz equal c_flux\[3\]/vol
|
|
fix JJ all ave/correlate $s $p $d &
|
|
c_flux\[1\] c_flux\[2\] c_flux\[3\] type auto file J0Jt.dat ave running
|
|
variable scale equal $\{convert\}/$\{kB\}/$T/$T/$V*$s*$\{dt\}
|
|
variable k11 equal trap(f_JJ\[3\])*$\{scale\}
|
|
variable k22 equal trap(f_JJ\[4\])*$\{scale\}
|
|
variable k33 equal trap(f_JJ\[5\])*$\{scale\}
|
|
thermo_style custom step temp v_Jx v_Jy v_Jz v_k11 v_k22 v_k33
|
|
run 100000
|
|
variable k equal (v_k11+v_k22+v_k33)/3.0
|
|
variable ndens equal count(all)/vol
|
|
print "average conductivity: $k\[W/mK\] @ $T K, $\{ndens\} /A^3" :pre
|