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67
doc/Section_howto.html
View File

@ -1915,11 +1915,15 @@ LAMMPS.
<A NAME = "howto_20"></A><H4>6.20 Calculating thermal conductivity
</H4>
<P>The thermal conductivity kappa of a material can be measured in at
least 3 ways using various options in LAMMPS. (See <A HREF = "Section_howto.html#howto_21">this
least 4 ways using various options in LAMMPS. See the examples/KAPPS
directory for scripts that implement the 4 methods discussed here for
a simple Lennard-Jones fluid model. Also, see <A HREF = "Section_howto.html#howto_21">this
section</A> of the manual for an analogous
discussion for viscosity). The thermal conducitivity tensor kappa is
a measure of the propensity of a material to transmit heat energy in a
diffusive manner as given by Fourier's law
discussion for viscosity.
</P>
<P>The thermal conducitivity tensor kappa is a measure of the propensity
of a material to transmit heat energy in a diffusive manner as given
by Fourier's law
</P>
<P>J = -kappa grad(T)
</P>
@ -1932,35 +1936,37 @@ scalar.
<P>The first method is to setup two thermostatted regions at opposite
ends of a simulation box, or one in the middle and one at the end of a
periodic box. By holding the two regions at different temperatures
with a <A HREF = "Section_howto.html#howto_13">thermostatting fix</A>, the energy added
to the hot region should equal the energy subtracted from the cold
region and be proportional to the heat flux moving between the
with a <A HREF = "Section_howto.html#howto_13">thermostatting fix</A>, the energy
added to the hot region should equal the energy subtracted from the
cold region and be proportional to the heat flux moving between the
regions. See the paper by <A HREF = "#Ikeshoji">Ikeshoji and Hafskjold</A> for
details of this idea. Note that thermostatting fixes such as <A HREF = "fix_nh.html">fix
nvt</A>, <A HREF = "fix_langevin.html">fix langevin</A>, and <A HREF = "fix_temp_rescale.html">fix
temp/rescale</A> store the cumulative energy they
add/subtract. Alternatively, the <A HREF = "fix_heat.html">fix heat</A> command can
used in place of thermostats on each of two regions, and the resulting
temperatures of the two regions monitored with the "compute
temp/region" command or the temperature profile of the intermediate
region monitored with the <A HREF = "fix_ave_spatial.html">fix ave/spatial</A> and
<A HREF = "compute_ke_atom.html">compute ke/atom</A> commands.
add/subtract. Alternatively, as a second method, the <A HREF = "fix_heat.html">fix
heat</A> command can used in place of thermostats on each
of two regions to add/subtract specified amounts of energy to both
regions. In both cases, the resulting temperatures of the two regions
can be monitored with the "compute temp/region" command and the
temperature profile of the intermediate region can be monitored with
the <A HREF = "fix_ave_spatial.html">fix ave/spatial</A> and <A HREF = "compute_ke_atom.html">compute
ke/atom</A> commands.
</P>
<P>The second method is to perform a reverse non-equilibrium MD
simulation using the <A HREF = "fix_thermal_conductivity.html">fix
thermal/conductivity</A> command which
implements the rNEMD algorithm of Muller-Plathe. Kinetic energy is
swapped between atoms in two different layers of the simulation box.
This induces a temperature gradient between the two layers which can
be monitored with the <A HREF = "fix_ave_spatial.html">fix ave/spatial</A> and
<A HREF = "compute_ke_atom.html">compute ke/atom</A> commands. The fix tallies the
<P>The third method is to perform a reverse non-equilibrium MD simulation
using the <A HREF = "fix_thermal_conductivity.html">fix thermal/conductivity</A>
command which implements the rNEMD algorithm of Muller-Plathe.
Kinetic energy is swapped between atoms in two different layers of the
simulation box. This induces a temperature gradient between the two
layers which can be monitored with the <A HREF = "fix_ave_spatial.html">fix
ave/spatial</A> and <A HREF = "compute_ke_atom.html">compute
ke/atom</A> commands. The fix tallies the
cumulative energy transfer that it performs. See the <A HREF = "fix_thermal_conductivity.html">fix
thermal/conductivity</A> command for
details.
</P>
<P>The third method is based on the Green-Kubo (GK) formula which relates
the ensemble average of the auto-correlation of the heat flux to
kappa. The heat flux can be calculated from the fluctuations of
<P>The fourth method is based on the Green-Kubo (GK) formula which
relates the ensemble average of the auto-correlation of the heat flux
to kappa. The heat flux can be calculated from the fluctuations of
per-atom potential and kinetic energies and per-atom stress tensor in
a steady-state equilibrated simulation. This is in contrast to the
two preceding non-equilibrium methods, where energy flows continuously
@ -1980,13 +1986,14 @@ formalism.
<A NAME = "howto_21"></A><H4>6.21 Calculating viscosity
</H4>
<P>The shear viscosity eta of a fluid can be measured in at least 3 ways
using various options in LAMMPS. (See <A HREF = "Section_howto.html#howto_20">this
using various options in LAMMPS. See <A HREF = "Section_howto.html#howto_20">this
section</A> of the manual for an analogous
discussion for thermal conductivity). Eta is a measure of the
propensity of a fluid to transmit momentum in a direction
perpendicular to the direction of velocity or momentum flow.
Alternatively it is the resistance the fluid has to being sheared. It
is given by
discussion for thermal conductivity.
</P>
<P>Eta is a measure of the propensity of a fluid to transmit momentum in
a direction perpendicular to the direction of velocity or momentum
flow. Alternatively it is the resistance the fluid has to being
sheared. It is given by
</P>
<P>J = -eta grad(Vstream)
</P>

67
doc/Section_howto.txt
View File

@ -1902,11 +1902,15 @@ LAMMPS.
6.20 Calculating thermal conductivity :link(howto_20),h4
The thermal conductivity kappa of a material can be measured in at
least 3 ways using various options in LAMMPS. (See "this
least 4 ways using various options in LAMMPS. See the examples/KAPPS
directory for scripts that implement the 4 methods discussed here for
a simple Lennard-Jones fluid model. Also, see "this
section"_Section_howto.html#howto_21 of the manual for an analogous
discussion for viscosity). The thermal conducitivity tensor kappa is
a measure of the propensity of a material to transmit heat energy in a
diffusive manner as given by Fourier's law
discussion for viscosity.
The thermal conducitivity tensor kappa is a measure of the propensity
of a material to transmit heat energy in a diffusive manner as given
by Fourier's law
J = -kappa grad(T)
@ -1919,35 +1923,37 @@ scalar.
The first method is to setup two thermostatted regions at opposite
ends of a simulation box, or one in the middle and one at the end of a
periodic box. By holding the two regions at different temperatures
with a "thermostatting fix"_Section_howto.html#howto_13, the energy added
to the hot region should equal the energy subtracted from the cold
region and be proportional to the heat flux moving between the
with a "thermostatting fix"_Section_howto.html#howto_13, the energy
added to the hot region should equal the energy subtracted from the
cold region and be proportional to the heat flux moving between the
regions. See the paper by "Ikeshoji and Hafskjold"_#Ikeshoji for
details of this idea. Note that thermostatting fixes such as "fix
nvt"_fix_nh.html, "fix langevin"_fix_langevin.html, and "fix
temp/rescale"_fix_temp_rescale.html store the cumulative energy they
add/subtract. Alternatively, the "fix heat"_fix_heat.html command can
used in place of thermostats on each of two regions, and the resulting
temperatures of the two regions monitored with the "compute
temp/region" command or the temperature profile of the intermediate
region monitored with the "fix ave/spatial"_fix_ave_spatial.html and
"compute ke/atom"_compute_ke_atom.html commands.
add/subtract. Alternatively, as a second method, the "fix
heat"_fix_heat.html command can used in place of thermostats on each
of two regions to add/subtract specified amounts of energy to both
regions. In both cases, the resulting temperatures of the two regions
can be monitored with the "compute temp/region" command and the
temperature profile of the intermediate region can be monitored with
the "fix ave/spatial"_fix_ave_spatial.html and "compute
ke/atom"_compute_ke_atom.html commands.
The second method is to perform a reverse non-equilibrium MD
simulation using the "fix
thermal/conductivity"_fix_thermal_conductivity.html command which
implements the rNEMD algorithm of Muller-Plathe. Kinetic energy is
swapped between atoms in two different layers of the simulation box.
This induces a temperature gradient between the two layers which can
be monitored with the "fix ave/spatial"_fix_ave_spatial.html and
"compute ke/atom"_compute_ke_atom.html commands. The fix tallies the
The third method is to perform a reverse non-equilibrium MD simulation
using the "fix thermal/conductivity"_fix_thermal_conductivity.html
command which implements the rNEMD algorithm of Muller-Plathe.
Kinetic energy is swapped between atoms in two different layers of the
simulation box. This induces a temperature gradient between the two
layers which can be monitored with the "fix
ave/spatial"_fix_ave_spatial.html and "compute
ke/atom"_compute_ke_atom.html commands. The fix tallies the
cumulative energy transfer that it performs. See the "fix
thermal/conductivity"_fix_thermal_conductivity.html command for
details.
The third method is based on the Green-Kubo (GK) formula which relates
the ensemble average of the auto-correlation of the heat flux to
kappa. The heat flux can be calculated from the fluctuations of
The fourth method is based on the Green-Kubo (GK) formula which
relates the ensemble average of the auto-correlation of the heat flux
to kappa. The heat flux can be calculated from the fluctuations of
per-atom potential and kinetic energies and per-atom stress tensor in
a steady-state equilibrated simulation. This is in contrast to the
two preceding non-equilibrium methods, where energy flows continuously
@ -1967,13 +1973,14 @@ formalism.
6.21 Calculating viscosity :link(howto_21),h4
The shear viscosity eta of a fluid can be measured in at least 3 ways
using various options in LAMMPS. (See "this
using various options in LAMMPS. See "this
section"_Section_howto.html#howto_20 of the manual for an analogous
discussion for thermal conductivity). Eta is a measure of the
propensity of a fluid to transmit momentum in a direction
perpendicular to the direction of velocity or momentum flow.
Alternatively it is the resistance the fluid has to being sheared. It
is given by
discussion for thermal conductivity.
Eta is a measure of the propensity of a fluid to transmit momentum in
a direction perpendicular to the direction of velocity or momentum
flow. Alternatively it is the resistance the fluid has to being
sheared. It is given by
J = -eta grad(Vstream)