Merge pull request #2019 from z-gong/viscosity

   * :doc:`torque/chunk <compute_torque_chunk>`

   * :doc:`torque/chunk <compute_torque_chunk>`

   * :doc:`vacf <compute_vacf>`

   * :doc:`vacf <compute_vacf>`

   * :doc:`vcm/chunk <compute_vcm_chunk>`

   * :doc:`vcm/chunk <compute_vcm_chunk>`

   * :doc:`viscosity/cos <compute_viscosity_cos>`

   * :doc:`voronoi/atom <compute_voronoi_atom>`

   * :doc:`voronoi/atom <compute_voronoi_atom>`

   * :doc:`xrd <compute_xrd>`

   * :doc:`xrd <compute_xrd>`

.. table_from_list::

.. table_from_list::

   :columns: 5

   :columns: 5

   * :doc:`accelerate/cos <fix_accelerate_cos>`

   * :doc:`adapt <fix_adapt>`

   * :doc:`adapt <fix_adapt>`

   * :doc:`adapt/fep <fix_adapt_fep>`

   * :doc:`adapt/fep <fix_adapt_fep>`

   * :doc:`addforce <fix_addforce>`

   * :doc:`addforce <fix_addforce>`

Calculate viscosity

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

using various options in LAMMPS.  See the examples/VISCOSITY directory

for scripts that implement the 5 methods discussed here for a simple

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.

thermal conductivity.

Eta is a measure of the propensity of a fluid to transmit momentum in

Eta is a measure of the propensity of a fluid to transmit momentum in

coordinates, whose mean-square displacement increases linearly

coordinates, whose mean-square displacement increases linearly

with time at sufficiently long times.

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 thermostatting.

.. note::

    An article by :ref:`(Hess) <Hess3>` discussed the accuracy and efficiency of these methods.

----------

----------

.. _Daivis-viscosity:

.. _Daivis-viscosity:

**(Daivis and Todd)** Daivis and Todd, Nonequilibrium Molecular Dynamics (book),

**(Daivis and Todd)** Daivis and Todd, Nonequilibrium Molecular Dynamics (book),

Cambridge University Press, https://doi.org/10.1017/9781139017848, (2017).

Cambridge University Press, https://doi.org/10.1017/9781139017848, (2017).

.. _Hess3:

**(Hess)** Hess, B. The Journal of Chemical Physics 2002, 116 (1), 209-217.

* :doc:`torque/chunk <compute_torque_chunk>` - torque applied on each chunk

* :doc:`torque/chunk <compute_torque_chunk>` - torque applied on each chunk

* :doc:`vacf <compute_vacf>` - velocity auto-correlation function of group of atoms

* :doc:`vacf <compute_vacf>` - velocity auto-correlation function of group of atoms

* :doc:`vcm/chunk <compute_vcm_chunk>` - velocity of center-of-mass for each chunk

* :doc:`vcm/chunk <compute_vcm_chunk>` - velocity of center-of-mass for each chunk

* :doc:`viscosity/cos <compute_viscosity_cos>` - velocity profile under cosine-shaped acceleration

* :doc:`voronoi/atom <compute_voronoi_atom>` - Voronoi volume and neighbors for each atom

* :doc:`voronoi/atom <compute_voronoi_atom>` - Voronoi volume and neighbors for each atom

* :doc:`xrd <compute_xrd>` - x-ray diffraction intensity on a mesh of reciprocal lattice nodes

* :doc:`xrd <compute_xrd>` - x-ray diffraction intensity on a mesh of reciprocal lattice nodes

.. index:: compute viscosity/cos

compute viscosity/cos command

=============================

Syntax

""""""

.. parsed-literal::

   compute ID group-ID viscosity/cos

* ID, group-ID are documented in :doc:`compute <compute>` command

* viscosity/cos = style name of this compute command

Examples

""""""""

.. code-block:: LAMMPS

   compute  cos all viscosity/cos

   variable V equal c_cos[7]

   variable A equal 0.02E-5

   variable density equal density

   variable lz equal lz

   variable reciprocalViscosity equal v_V/${A}/v_density*39.4784/v_lz/v_lz*100

Description

"""""""""""

Define a computation that calculates the velocity amplitude of a group of atoms

with an cosine-shaped velocity profile and the temperature of them

after subtracting out the velocity profile before computing the kinetic energy.

A compute of this style can be used by any command that computes a temperature,

e.g. :doc:`thermo_modify <thermo_modify>`, :doc:`fix npt <fix_nh>`, etc.

This command together with :doc:`fix_accelerate/cos<fix_accelerate_cos>`

enables viscosity calculation with periodic perturbation method,

as described by :ref:`Hess<Hess1>`.

An acceleration along the x-direction is applied to the simulation system

by using :doc:`fix_accelerate/cos<fix_accelerate_cos>` command.

The acceleration is a periodic function along the z-direction:

.. math::

   a_{x}(z) = A \cos \left(\frac{2 \pi z}{l_{z}}\right)

where :math:`A` is the acceleration amplitude, :math:`l_z` is the z-length

of the simulation box. At steady state, the acceleration generates

a velocity profile:

.. math::

   v_{x}(z) = V \cos \left(\frac{2 \pi z}{l_{z}}\right)

The generated velocity amplitude :math:`V` is related to the

shear viscosity :math:`\eta` by:

.. math::

   V = \frac{A \rho}{\eta}\left(\frac{l_{z}}{2 \pi}\right)^{2}

and it can be obtained from ensemble average of the velocity profile:

.. math::

   V = \frac{\sum_i 2 m_{i} v_{i, x} \cos \left(\frac{2 \pi z_i}{l_{z}}\right)}{\sum_i m_{i}}

where :math:`m_i`, :math:`v_{i,x}` and :math:`z_i` are the mass,

x-component velocity and z coordinate of a particle.

After the cosine-shaped collective velocity in :math:`x` direction

has been subtracted for each atom, the temperature is calculated by the formula

KE = dim/2 N k T, where KE = total kinetic energy of the group of

atoms (sum of 1/2 m v\^2), dim = 2 or 3 = dimensionality of the

simulation, N = number of atoms in the group, k = Boltzmann constant,

and T = temperature.

A kinetic energy tensor, stored as a 6-element vector, is also

calculated by this compute for use in the computation of a pressure

tensor. The formula for the components of the tensor is the same as

the above formula, except that v\^2 is replaced by vx\*vy for the xy

component, etc. The 6 components of the vector are ordered xx, yy,

zz, xy, xz, yz.

The number of atoms contributing to the temperature is assumed to be

constant for the duration of the run; use the *dynamic* option of the

:doc:`compute_modify <compute_modify>` command if this is not the case.

However, in order to get meaningful result, the group ID of this compute should be all.

The removal of the cosine-shaped velocity component by this command is

essentially computing the temperature after a "bias" has been removed

from the velocity of the atoms.  If this compute is used with a fix

command that performs thermostatting then this bias will be subtracted

from each atom, thermostatting of the remaining thermal velocity will

be performed, and the bias will be added back in.  Thermostatting

fixes that work in this way include :doc:`fix nvt <fix_nh>`, :doc:`fix temp/rescale <fix_temp_rescale>`, :doc:`fix temp/berendsen <fix_temp_berendsen>`, and :doc:`fix langevin <fix_langevin>`.

This compute subtracts out degrees-of-freedom due to fixes that

constrain molecular motion, such as :doc:`fix shake <fix_shake>` and

:doc:`fix rigid <fix_rigid>`.  This means the temperature of groups of

atoms that include these constraints will be computed correctly.  If

needed, the subtracted degrees-of-freedom can be altered using the

*extra* option of the :doc:`compute_modify <compute_modify>` command.

See the :doc:`Howto thermostat <Howto_thermostat>` doc page for a

discussion of different ways to compute temperature and perform

thermostatting.

----------

**Output info:**

This compute calculates a global scalar (the temperature) and a global

vector of length 7, which can be accessed by indices 1-7.

The first 6 elements of the vector are the KE tensor,

and the 7-th is the cosine-shaped velocity amplitude :math:`V`,

which can be used to calculate the reciprocal viscosity, as shown in the example.

These values can be used by any command that uses global scalar or

vector values from a compute as input.

See the :doc:`Howto output <Howto_output>` doc page for an overview of LAMMPS output options.

The scalar value calculated by this compute is "intensive".  The

first 6 elements of vector values are "extensive",

and the 7-th element of vector values is "intensive".

The scalar value will be in temperature :doc:`units <units>`.  The

first 6 elements of vector values will be in energy :doc:`units <units>`.

The 7-th element of vector value will be in velocity :doc:`units <units>`.

Restrictions

""""""""""""

This command is only available when LAMMPS was built with the USER-MISC package.

Since this compute depends on :doc:`fix accelerate/cos <fix_accelerate_cos>` which can

only work for 3d systems, it cannot be used for 2d systems.

Related commands

""""""""""""""""

:doc:`fix accelerate/cos <fix_accelerate_cos>`

Default

"""""""

 none

----------

.. _Hess1:

**(Hess)** Hess, B. The Journal of Chemical Physics 2002, 116 (1), 209-217.