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75
doc/Section_howto.html
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@ -1915,7 +1915,7 @@ 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 4 ways using various options in LAMMPS. See the examples/KAPPS
least 4 ways using various options in LAMMPS. See the examples/KAPPA
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
@ -1943,13 +1943,15 @@ 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, 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
add/subtract.
</P>
<P>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 third method is to perform a reverse non-equilibrium MD simulation
@ -1985,8 +1987,10 @@ 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
<P>The shear viscosity eta of a fluid can be measured in at least 4 ways
using various options in LAMMPS. See the examples/VISCOSITY 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_20">this
section</A> of the manual for an analogous
discussion for thermal conductivity.
</P>
@ -2005,33 +2009,38 @@ momentum flows. Viscosity thus has units of pressure-time.
<P>The first method is to perform a non-equlibrium MD (NEMD) simulation
by shearing the simulation box via the <A HREF = "fix_deform.html">fix deform</A>
command, and using the <A HREF = "fix_nvt_sllod.html">fix nvt/sllod</A> command to
thermostat the fluid via the SLLOD equations of motion. The velocity
profile setup in the fluid by this procedure can be monitored by the
<A HREF = "fix_ave_spatial.html">fix ave/spatial</A> command, which determines
thermostat the fluid via the SLLOD equations of motion.
Alternatively, as a second method, one or more moving walls can be
used to shear the fluid in between them, again with some kind of
thermostat that modifies only the thermal (non-shearing) components of
velocity to prevent the fluid from heating up.
</P>
<P>In both cases, the velocity profile setup in the fluid by this
procedure can be monitored by the <A HREF = "fix_ave_spatial.html">fix
ave/spatial</A> command, which determines
grad(Vstream) in the equation above. E.g. the derivative in the
y-direction of the Vx component of fluid motion or grad(Vstream) =
dVx/dy. In this case, the Pxy off-diagonal component of the pressure
or stress tensor, as calculated by the <A HREF = "compute_pressure.html">compute
pressure</A> command, can also be monitored, which
is the J term in the equation above. See <A HREF = "Section_howto.html#howto_13">this
section</A> of the manual for details on NEMD
simulations.
dVx/dy. The Pxy off-diagonal component of the pressure or stress
tensor, as calculated by the <A HREF = "compute_pressure.html">compute pressure</A>
command, can also be monitored, which is the J term in the equation
above. See <A HREF = "Section_howto.html#howto_13">this section</A> of the manual
for details on NEMD simulations.
</P>
<P>The second method is to perform a reverse non-equilibrium MD
simulation using the <A HREF = "fix_viscosity.html">fix viscosity</A> command which
implements the rNEMD algorithm of Muller-Plathe. Momentum in one
dimension is swapped between atoms in two different layers of the
simulation box in a different dimension. This induces a velocity
gradient which can be monitored with the <A HREF = "fix_ave_spatial.html">fix
ave/spatial</A> command. The fix tallies the
cummulative momentum transfer that it performs. See the <A HREF = "fix_viscosity.html">fix
viscosity</A> command for details.
<P>The third method is to perform a reverse non-equilibrium MD simulation
using the <A HREF = "fix_viscosity.html">fix viscosity</A> command which implements
the rNEMD algorithm of Muller-Plathe. Momentum in one dimension is
swapped between atoms in two different layers of the simulation box in
a different dimension. This induces a velocity gradient which can be
monitored with the <A HREF = "fix_ave_spatial.html">fix ave/spatial</A> command.
The fix tallies the cummulative momentum transfer that it performs.
See the <A HREF = "fix_viscosity.html">fix viscosity</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 stress/pressure
tensor to eta. This can be done in a steady-state equilibrated
simulation which is in contrast to the two preceding non-equilibrium
methods, where momentum flows continuously through the simulation box.
<P>The fourth method is based on the Green-Kubo (GK) formula which
relates the ensemble average of the auto-correlation of the
stress/pressure tensor to eta. This can be done in a steady-state
equilibrated simulation which is in contrast to the two preceding
non-equilibrium methods, where momentum flows continuously through the
simulation box.
</P>
<P>Here is an example input script that calculates the viscosity of
liquid Ar via the GK formalism:

75
doc/Section_howto.txt
View File

@ -1902,7 +1902,7 @@ LAMMPS.
6.20 Calculating thermal conductivity :link(howto_20),h4
The thermal conductivity kappa of a material can be measured in at
least 4 ways using various options in LAMMPS. See the examples/KAPPS
least 4 ways using various options in LAMMPS. See the examples/KAPPA
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
@ -1930,13 +1930,15 @@ 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, 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
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 third method is to perform a reverse non-equilibrium MD simulation
@ -1972,8 +1974,10 @@ 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
The shear viscosity eta of a fluid can be measured in at least 4 ways
using various options in LAMMPS. See the examples/VISCOSITY 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_20 of the manual for an analogous
discussion for thermal conductivity.
@ -1992,33 +1996,38 @@ momentum flows. Viscosity thus has units of pressure-time.
The first method is to perform a non-equlibrium MD (NEMD) simulation
by shearing the simulation box via the "fix deform"_fix_deform.html
command, and using the "fix nvt/sllod"_fix_nvt_sllod.html command to
thermostat the fluid via the SLLOD equations of motion. The velocity
profile setup in the fluid by this procedure can be monitored by the
"fix ave/spatial"_fix_ave_spatial.html command, which determines
thermostat the fluid via the SLLOD equations of motion.
Alternatively, as a second method, one or more moving walls can be
used to shear the fluid in between them, again with some kind of
thermostat that modifies only the thermal (non-shearing) components of
velocity to prevent the fluid from heating up.
In both cases, the velocity profile setup in the fluid by this
procedure can be monitored by the "fix
ave/spatial"_fix_ave_spatial.html command, which determines
grad(Vstream) in the equation above. E.g. the derivative in the
y-direction of the Vx component of fluid motion or grad(Vstream) =
dVx/dy. In this case, the Pxy off-diagonal component of the pressure
or stress tensor, as calculated by the "compute
pressure"_compute_pressure.html command, can also be monitored, which
is the J term in the equation above. See "this
section"_Section_howto.html#howto_13 of the manual for details on NEMD
simulations.
dVx/dy. The Pxy off-diagonal component of the pressure or stress
tensor, as calculated by the "compute pressure"_compute_pressure.html
command, can also be monitored, which is the J term in the equation
above. See "this section"_Section_howto.html#howto_13 of the manual
for details on NEMD simulations.
The second method is to perform a reverse non-equilibrium MD
simulation using the "fix viscosity"_fix_viscosity.html command which
implements the rNEMD algorithm of Muller-Plathe. Momentum in one
dimension is swapped between atoms in two different layers of the
simulation box in a different dimension. This induces a velocity
gradient which can be monitored with the "fix
ave/spatial"_fix_ave_spatial.html command. The fix tallies the
cummulative momentum transfer that it performs. See the "fix
viscosity"_fix_viscosity.html command for details.
The third method is to perform a reverse non-equilibrium MD simulation
using the "fix viscosity"_fix_viscosity.html command which implements
the rNEMD algorithm of Muller-Plathe. Momentum in one dimension is
swapped between atoms in two different layers of the simulation box in
a different dimension. This induces a velocity gradient which can be
monitored with the "fix ave/spatial"_fix_ave_spatial.html command.
The fix tallies the cummulative momentum transfer that it performs.
See the "fix viscosity"_fix_viscosity.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 stress/pressure
tensor to eta. This can be done in a steady-state equilibrated
simulation which is in contrast to the two preceding non-equilibrium
methods, where momentum flows continuously through the simulation box.
The fourth method is based on the Green-Kubo (GK) formula which
relates the ensemble average of the auto-correlation of the
stress/pressure tensor to eta. This can be done in a steady-state
equilibrated simulation which is in contrast to the two preceding
non-equilibrium methods, where momentum flows continuously through the
simulation box.
Here is an example input script that calculates the viscosity of
liquid Ar via the GK formalism: