From 4fe160c56ec24687bd505d75cd74e7d4fbd43fe8 Mon Sep 17 00:00:00 2001 From: sjplimp Date: Thu, 12 Sep 2013 23:37:43 +0000 Subject: [PATCH] git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@10775 f3b2605a-c512-4ea7-a41b-209d697bcdaa --- doc/Section_howto.html | 75 +++++++++++++++++++++++------------------- doc/Section_howto.txt | 75 +++++++++++++++++++++++------------------- 2 files changed, 84 insertions(+), 66 deletions(-) diff --git a/doc/Section_howto.html b/doc/Section_howto.html index 967ee19a78..74f4917096 100644 --- a/doc/Section_howto.html +++ b/doc/Section_howto.html @@ -1915,7 +1915,7 @@ LAMMPS.

6.20 Calculating thermal conductivity

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.

6.21 Calculating viscosity

-

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.

@@ -2005,33 +2009,38 @@ 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 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: