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 of the manual for an analogous @@ -1943,13 +1943,15 @@ regions. See the paper by Ikeshoji and Hafskjold for details of this idea. Note that thermostatting fixes such as fix nvt, fix langevin, and fix temp/rescale store the cumulative energy they -add/subtract. Alternatively, as a second method, the fix -heat 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 and compute +add/subtract. +
+Alternatively, as a second method, the fix heat +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 and compute ke/atom commands.
The third method is to perform a reverse non-equilibrium MD simulation @@ -1985,8 +1987,10 @@ formalism.
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 of the manual for an analogous
discussion for thermal conductivity.
The first method is to perform a non-equlibrium MD (NEMD) simulation
by shearing the simulation box via the fix deform
command, and using the fix nvt/sllod 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 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 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 command, can also be monitored, which
-is the J term in the equation above. See this
-section 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
+command, can also be monitored, which is the J term in the equation
+above. See this section of the manual
+for details on NEMD simulations.
The second method is to perform a reverse non-equilibrium MD
-simulation using the fix viscosity 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 command. The fix tallies the
-cummulative momentum transfer that it performs. See the fix
-viscosity command for details.
+ The third method is to perform a reverse non-equilibrium MD simulation
+using the fix viscosity 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 command.
+The fix tallies the cummulative momentum transfer that it performs.
+See the fix viscosity 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:
diff --git a/doc/Section_howto.txt b/doc/Section_howto.txt
index 3355469781..9d1ba9911b 100644
--- a/doc/Section_howto.txt
+++ b/doc/Section_howto.txt
@@ -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: