Update How-to viscosity and put the example together with other viscosity examples.

doc/src/Howto_viscosity.rst

@@ -1,10 +1,11 @@
 Calculate viscosity
 ===================
 
-The shear viscosity eta of a fluid can be measured in at least 5 ways
+The shear viscosity eta of a fluid can be measured in at least 6 ways
 using various options in LAMMPS.  See the examples/VISCOSITY directory
 for scripts that implement the 5 methods discussed here for a simple
-Lennard-Jones fluid model.  Also, see the :doc:`Howto kappa <Howto_kappa>` doc page for an analogous discussion for
+Lennard-Jones fluid model and 1 method for SPC/E water model.
+Also, see the :doc:`Howto kappa <Howto_kappa>` doc page for an analogous discussion for
 thermal conductivity.
 
 Eta is a measure of the propensity of a fluid to transmit momentum in
@@ -130,9 +131,24 @@ time-integrated momentum fluxes play the role of Cartesian
 coordinates, whose mean-square displacement increases linearly
 with time at sufficiently long times.
 
+The sixth is periodic perturbation method. It is also a non-equilibrium MD method.
+However, instead of measure the momentum flux in response of applied velocity gradient,
+it measures the velocity profile in response of applied stress.
+A cosine-shaped periodic acceleration is added to the system via the
+:doc:`fix accelerate/cos <fix_accelerate_cos>` command,
+and the :doc:`compute viscosity/cos<compute_viscosity_cos>` command is used to monitor the
+generated velocity profile and remove the velocity bias before thermostating.
+
+.. note::
+
+    An article by :ref:`(Hess) <Hess3>` discussed the accuracy and efficiency of these methods.
+
 ----------
 
 .. _Daivis-viscosity:
 
 **(Daivis and Todd)** Daivis and Todd, Nonequilibrium Molecular Dynamics (book),
 Cambridge University Press, https://doi.org/10.1017/9781139017848, (2017).
+
+.. _Hess3:
+**(Hess)** Hess, B. The Journal of Chemical Physics 2002, 116 (1), 209-217.

examples/USER/misc/viscosity/README

@@ -1,5 +0,0 @@
-The input script in in.1000SPCE.lmp gives an example on how to calculate
-the shear viscosity of SPCE water with the periodic perturbation method.
-For a production run, much longer simulation is required.
-Note that the acceleration amplitude of `fix accelerate/cos` should be carefully chosen,
-and an extrapolation is generally required to get the viscosity at zero-shear.

examples/VISCOSITY/README

@@ -1,5 +1,6 @@
-This directory has 5 scripts that compute the viscosity (eta) of a
+This directory has 6 scripts that compute the viscosity (eta) of fluid
-Lennard-Jones fluid using 5 different methods.  See the discussion in
+using 6 different methods. 5 of them are for a Lennard-Jones fluid
+and the last one is for SPC/E water model. See the discussion in
 Section 6.21 of the manual for an overview of the methods and pointers
 to doc pages for the commands which implement them.  Citations for the
 various methods can also be found in the manual.
@@ -10,7 +11,7 @@ enough to generate good statistics and highly accurate results.
 
 -------------
 
-These are the 5 methods for computing viscosity.  The first 3 are
+These are the 5 methods for computing viscosity of a LJ fluid.  The first 3 are
 non-equilibrium methods; the last 2 are equilibrium methods.
 
 in.wall = move a wall to shear the fluid between two walls
@@ -89,3 +90,18 @@ heat/flux doc page - the resulting value prints at the end of the run
 and is in the log file
 
 eta = 1.07
+
+-------------
+
+in.cos.1000SPCE is an example script of using cosine periodic perturbation method
+to calculate the viscosity of SPC/E water model.
+
+The reciprocal of eta is computed within the script, and printed out as v_invVis
+in thermo_style command. The result will converge after hundreds of picoseconds.
+Then eta is obtained from the reciprocal of time average of v_invVis.
+
+eta = 0.75 mPa*s
+
+Note that the calculated viscosity by this method decreases with increased acceleration.
+It is therefore generally necessary to perform calculation at different accelerations
+and extrapolate the viscosity to zero shear.

examples/VISCOSITY/in.cos.1000SPCE

@@ -15,7 +15,7 @@ angle_style    harmonic
 dihedral_style none
 improper_style none
 
-read_data      data.1000SPCE.lmp
+read_data      data.cos.1000SPCE
 
 variable T equal 300
 variable P equal 1.0
@@ -29,7 +29,7 @@ fix com        all momentum 100 linear 1 1 1
 fix rigid      all shake 1e-4 20 0 b 1 a 1
 
 # Viscosity  ##################################
-variable       A equal 0.02e-5 # angstrom/fs^2
+variable       A equal 0.05e-5 # angstrom/fs^2
 
 fix            cos all accelerate/cos ${A}
 compute        cos all viscosity/cos