ICODE-ADC/lammps
4
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

update compute heat/flux documentation

Browse Source
This commit is contained in:
Donatas Surblys
2019-11-12 22:43:52 +09:00
parent 5ba7686939
commit b65a3e94a7
1 changed files with 67 additions and 25 deletions
Download Patch File Download Diff File Expand all files Collapse all files

88
doc/src/compute_heat_flux.rst
View File

@ -54,38 +54,58 @@ third calculates per-atom stress (\ *stress-ID*\ ).
(or any group whose atoms are superset of the atoms in this compute's
group). LAMMPS does not check for this.
The Green-Kubo formulas relate the ensemble average of the
auto-correlation of the heat flux J to the thermal conductivity kappa:
In case of pairwise interactions the heat flux is defined as:
.. image:: Eqs/heat_flux_J.jpg
:align: center
.. math::
\mathbf{J} &= \frac{1}{V} \left[ \sum_i e_i \mathbf{v}_i - \sum_{i} \mathbf{S}_{i} \mathbf{v}_i \right] \\
&= \frac{1}{V} \left[ \sum_i e_i \mathbf{v}_i + \sum_{i<j} \left( \mathbf{F}_{ij} \cdot \mathbf{v}_j \right) \mathbf{r}_{ij} \right] \\
&= \frac{1}{V} \left[ \sum_i e_i \mathbf{v}_i + \frac{1}{2} \sum_{i<j} \left( \mathbf{F}_{ij} \cdot \left(\mathbf{v}_i + \mathbf{v}_j \right) \right) \mathbf{r}_{ij} \right]
.. image:: Eqs/heat_flux_k.jpg
:align: center
Ei in the first term of the equation for J is the per-atom energy
(potential and kinetic). This is calculated by the computes *ke-ID*
and *pe-ID*\ . Si in the second term of the equation for J is the
per-atom stress tensor calculated by the compute *stress-ID*\ . The
tensor multiplies Vi as a 3x3 matrix-vector multiply to yield a
vector. Note that as discussed below, the 1/V scaling factor in the
equation for J is NOT included in the calculation performed by this
compute; you need to add it for a volume appropriate to the atoms
:math:`e_i` in the first term of the equation
is the per-atom energy (potential and kinetic).
This is calculated by the computes *ke-ID*
and *pe-ID*. :math:`\mathbf{S}_i` in the second term is the
per-atom stress tensor calculated by the compute *stress-ID*.
See :doc:`compute stress/atom <compute_stress_atom>`
and :doc:`compute centroid/stress/atom <compute_stress_atom>`
for possible definitions of atomic stress :math:`\mathbf{S}_i`
in the case of thee-body and larger many-body interactions.
The tensor multiplies :math:`\mathbf{v}_i` as a 3x3 matrix-vector multiply
to yield a vector.
Note that as discussed below, the :math:`\frac{1}{V}` scaling factor in the
equation for :math:`\mathbf{J}` is NOT included in the calculation performed by
these computes; you need to add it for a volume appropriate to the atoms
included in the calculation.
.. note::
The :doc:`compute pe/atom <compute_pe_atom>` and :doc:`compute stress/atom <compute_stress_atom>` commands have options for which
The :doc:`compute pe/atom <compute_pe_atom>` and
:doc:`compute stress/atom <compute_stress_atom>`
commands have options for which
terms to include in their calculation (pair, bond, etc). The heat
flux calculation will thus include exactly the same terms. Normally
you should use :doc:`compute stress/atom virial <compute_stress_atom>`
or :doc:`compute centroid/stress/atom virial <compute_stress_atom>`
so as not to include a kinetic energy term in the heat flux.
This compute calculates 6 quantities and stores them in a 6-component
vector. The first 3 components are the x, y, z components of the full
heat flux vector, i.e. (Jx, Jy, Jz). The next 3 components are the x,
y, z components of just the convective portion of the flux, i.e. the
first term in the equation for J above.
.. warning::
The compute *heat/flux* has been reported to produce unphysical
values for three and larger many-body interactions such
as angles, dihedrals and torsions,
when used with :doc:`compute stress/atom <compute_stress_atom>`,
as discussed in :ref:`(Surblys) <Surblys2>` and :ref:`(Boone) <Boone>`.
You are strongly advised to
use :doc:`compute centroid/stress/atom <compute_stress_atom>`,
which has been implemented specifically for such cases.
The Green-Kubo formulas relate the ensemble average of the
auto-correlation of the heat flux :math:`\mathbf{J}`
to the thermal conductivity :math:`\kappa`:
.. math::
\kappa = \frac{V}{k_B T^2} \int_0^\infty \langle J_x(0) J_x(t) \rangle \, \mathrm{d} t = \frac{V}{3 k_B T^2} \int_0^\infty \langle \mathbf{J}(0) \cdot \mathbf{J}(t) \rangle \, \mathrm{d}t
----------
@ -109,8 +129,14 @@ result should be: average conductivity ~0.29 in W/mK.
**Output info:**
This compute calculates a global vector of length 6 (total heat flux
vector, followed by convective heat flux vector), which can be
This compute calculates a global vector of length 6.
The first 3 components are the :math:`x`, :math:`y`, :math:`z`
components of the full heat flux vector,
i.e. (:math:`J_x`, :math:`J_y`, :math:`J_z`).
The next 3 components are the :math:`x`, :math:`y`, :math:`z` components
of just the convective portion of the flux, i.e. the
first term in the equation for :math:`\mathbf{J}`.
Each component can be
accessed by indices 1-6. These values can be used by any command that
uses global vector values from a compute as input. See the :doc:`Howto output <Howto_output>` doc page for an overview of LAMMPS output
options.
@ -212,6 +238,22 @@ Related commands
print "average conductivity: $k[W/mK] @ $T K, ${ndens} /A\^3"
----------
.. _Surblys2:
**(Surblys)** Surblys, Matsubara, Kikugawa, Ohara, Phys Rev E, 99, 051301(R) (2019).
.. _Boone:
**(Boone)** Boone, Babaei, Wilmer, J Chem Theory Comput, 15, 5579--5587 (2019).
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html