2009-07-03 00:38:31 +08:00
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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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<HR>
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<H3>compute heat/flux command
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</H3>
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<P><B>Syntax:</B>
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</P>
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2010-03-30 07:59:34 +08:00
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<PRE>compute ID group-ID heat/flux ke-ID pe-ID stress-ID
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2009-07-03 00:38:31 +08:00
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</PRE>
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<UL><LI>ID, group-ID are documented in <A HREF = "compute.html">compute</A> command
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<LI>heat/flux = style name of this compute command
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2010-03-30 07:59:34 +08:00
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<LI>ke-ID = ID of a compute that calculates per-atom kinetic energy
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<LI>pe-ID = ID of a compute that calculates per-atom potential energy
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<LI>stress-ID = ID of a compute that calculates per-atom stress
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2009-07-03 00:38:31 +08:00
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</UL>
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<P><B>Examples:</B>
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</P>
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2010-03-30 07:59:34 +08:00
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<PRE>compute myFlux all heat/flux myKE myPE myStress
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2009-07-03 00:38:31 +08:00
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>Define a computation that calculates the heat flux vector based on
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2010-03-30 07:59:34 +08:00
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contributions from atoms in the specified group. This can be used by
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itself to measure the heat flux into or out of a reservoir of atoms,
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or to calculate a thermal conductivity using the Green-Kubo formalism.
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2009-07-03 00:38:31 +08:00
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</P>
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2009-07-03 00:40:58 +08:00
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<P>See the <A HREF = "fix_thermal_conductivity.html">fix thermal/conductivity</A>
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command for details on how to compute thermal conductivity in an
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2010-05-07 23:11:21 +08:00
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alternate way, via the Muller-Plathe method. See the <A HREF = "fix_heat.html">fix
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2010-03-30 07:59:34 +08:00
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heat</A> command for a way to control the heat added or
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subtracted to a group of atoms.
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2009-07-03 00:40:58 +08:00
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</P>
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2010-03-30 07:59:34 +08:00
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<P>The compute takes three arguments which are IDs of other
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<A HREF = "compute.html">computes</A>. One calculates per-atom kinetic energy
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(<I>ke-ID</I>), one calculates per-atom potential energy (<I>pe-ID)</I>, and the
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third calcualtes per-atom stress (<I>stress-ID</I>). These should be
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defined for the same group used by compute heat/flux, though LAMMPS
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does not check for this.
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2009-07-03 00:38:31 +08:00
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</P>
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<P>The Green-Kubo formulas relate the ensemble average of the
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2010-03-30 07:59:34 +08:00
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auto-correlation of the heat flux J to the thermal conductivity kappa:
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2009-07-03 00:38:31 +08:00
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</P>
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<CENTER><IMG SRC = "Eqs/heat_flux_J.jpg">
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</CENTER>
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2010-03-30 07:59:34 +08:00
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<CENTER><IMG SRC = "Eqs/heat_flux_k.jpg">
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</CENTER>
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<P>Ei in the first term of the equation for J is the per-atom energy
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(potential and kinetic). This is calculated by the computes <I>ke-ID</I>
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and <I>pe-ID</I>. Si in the second term of the equation for J is the
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per-atom stress tensor calculated by the compute <I>stress-ID</I>. The
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2010-03-30 08:20:14 +08:00
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tensor multiplies Vi as a 3x3 matrix-vector multiply to yield a
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2010-03-30 07:59:34 +08:00
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vector. Note that as discussed below, the 1/V scaling factor in the
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equation for J is NOT included in the calculation performed by this
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compute; you need to add it for a volume appropriate to the atoms
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included in the calculation.
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</P>
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<P>IMPORTANT NOTE: The <A HREF = "compute_pe_atom.html">compute pe/atom</A> and
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<A HREF = "compute_stress_atom.html">compute stress/atom</A> commands have options
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for which terms to include in their calculation (pair, bond, etc).
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The heat flux calculation will thus include exactly the same terms.
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2010-04-26 21:54:11 +08:00
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Normally you should use <A HREF = "compute_stress_atom.html">compute stress/atom
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virial</A> so as not to include a kinetic energy
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term in the heat flux. Note that neither of those computes is able to
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include a long-range Coulombic contribution to the per-atom energy or
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stress.
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2010-03-30 07:59:34 +08:00
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</P>
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<P>This compute calculates 6 quantities and stores them in a 6-component
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vector. The first 3 components are the x, y, z components of the full
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heat flux vector, i.e. (Jx, Jy, Jz). The next 3 components are the x,
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y, z components of just the convective portion of the flux, i.e. the
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first term in the equation for J above.
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2010-01-24 07:20:05 +08:00
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</P>
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<HR>
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2010-03-30 07:59:34 +08:00
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<P>The heat flux can be output every so many timesteps (e.g. via the
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<A HREF = "thermo_style.html">thermo_style custom</A> command). Then as a
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post-processing operation, an autocorrelation can be performed, its
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integral estimated, and the Green-Kubo formula above evaluated.
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2009-07-03 00:38:31 +08:00
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</P>
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2010-08-20 00:16:31 +08:00
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<P>The <A HREF = "fix_ave_correlate.html">fix ave/correlate</A> command can calclate
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the autocorrelation. The trap() function in the
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<A HREF = "variable.html">variable</A> command can calculate the integral.
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2010-03-30 07:59:34 +08:00
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</P>
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2011-01-04 00:42:55 +08:00
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<P>An example LAMMPS input script for solid Ar is appended below. The
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result should be: average conductivity ~0.29 in W/mK.
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2010-03-30 07:59:34 +08:00
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</P>
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<HR>
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<P><B>Output info:</B>
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2009-07-03 00:38:31 +08:00
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</P>
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2010-03-30 07:59:34 +08:00
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<P>This compute calculates a global vector of length 6 (total heat flux
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vector, followed by conductive heat flux vector), which can be
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accessed by indices 1-6. These values can be used by any command that
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uses global vector values from a compute as input. See <A HREF = "Section_howto.html#howto_15">this
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section</A> for an overview of LAMMPS output
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options.
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2010-01-24 07:20:05 +08:00
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</P>
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2010-03-30 07:59:34 +08:00
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<P>The vector values calculated by this compute are "extensive", meaning
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they scale with the number of atoms in the simulation. They can be
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divided by the appropriate volume to get a flux, which would then be
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an "intensive" value, meaning independent of the number of atoms in
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the simulation. Note that if the compute is "all", then the
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appropriate volume to divide by is the simulation box volume.
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However, if a sub-group is used, it should be the volume containing
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those atoms.
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2009-07-03 00:38:31 +08:00
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</P>
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<P>The vector values will be in energy*velocity <A HREF = "units.html">units</A>. Once
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divided by a volume the units will be that of flux, namely
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energy/area/time <A HREF = "units.html">units</A>
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</P>
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<P><B>Restrictions:</B> none
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</P>
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<P><B>Related commands:</B>
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</P>
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2010-08-20 00:16:31 +08:00
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<P><A HREF = "fix_thermal_conductivity.html">fix thermal/conductivity</A>,
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<A HREF = "fix_ave_correlate.html">fix ave/correlate</A>,
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<A HREF = "variable.html">variable</A>
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2009-07-03 00:38:31 +08:00
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</P>
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<P><B>Default:</B> none
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</P>
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<HR>
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2011-01-04 00:42:55 +08:00
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<PRE># Sample LAMMPS input script for thermal conductivity of solid Ar
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</PRE>
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<PRE>units real
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variable T equal 70
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variable V equal vol
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variable dt equal 4.0
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variable p equal 200 # correlation length
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variable s equal 10 # sample interval
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variable d equal $p*$s # dump interval
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</PRE>
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<PRE># convert from LAMMPS real units to SI
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</PRE>
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<PRE>variable kB equal 1.3806504e-23 # [J/K] Boltzmann
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variable kCal2J equal 4186.0/6.02214e23
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variable A2m equal 1.0e-10
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variable fs2s equal 1.0e-15
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variable convert equal ${kCal2J}*${kCal2J}/${fs2s}/${A2m}
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</PRE>
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<PRE># setup problem
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</PRE>
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<PRE>dimension 3
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boundary p p p
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lattice fcc 5.376 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
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region box block 0 4 0 4 0 4
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create_box 1 box
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create_atoms 1 box
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mass 1 39.948
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pair_style lj/cut 13.0
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pair_coeff * * 0.2381 3.405
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2010-08-30 22:25:37 +08:00
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timestep ${dt}
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thermo $d
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2009-07-03 00:38:31 +08:00
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</PRE>
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2011-01-04 00:42:55 +08:00
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<PRE># equilibration and thermalization
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2009-07-03 00:38:31 +08:00
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</PRE>
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2011-01-04 00:42:55 +08:00
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<PRE>velocity all create $T 102486 mom yes rot yes dist gaussian
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fix NVT all nvt temp $T $T 10 drag 0.2
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run 8000
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</PRE>
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<PRE># thermal conductivity calculation, switch to NVE if desired
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</PRE>
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<PRE>#unfix NVT
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#fix NVE all nve
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2010-12-18 02:14:26 +08:00
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</PRE>
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2011-01-04 00:42:55 +08:00
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<PRE>reset_timestep 0
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compute myKE all ke/atom
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compute myPE all pe/atom
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compute myStress all stress/atom virial
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compute flux all heat/flux myKE myPE myStress
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variable Jx equal c_flux[1]/vol
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variable Jy equal c_flux[2]/vol
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variable Jz equal c_flux[3]/vol
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fix JJ all ave/correlate $s $p $d &
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c_flux[1] c_flux[2] c_flux[3] type auto file J0Jt.dat ave running
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variable scale equal ${convert}/${kB}/$T/$T/$V*$s*${dt}
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variable k11 equal trap(f_JJ[3])*${scale}
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variable k22 equal trap(f_JJ[4])*${scale}
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variable k33 equal trap(f_JJ[5])*${scale}
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2010-08-20 00:16:31 +08:00
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thermo_style custom step temp v_Jx v_Jy v_Jz v_k11 v_k22 v_k33
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2011-01-04 00:42:55 +08:00
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run 100000
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variable k equal (v_k11+v_k22+v_k33)/3.0
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variable ndens equal count(all)/vol
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print "average conductivity: $k[W/mK] @ $T K, ${ndens} /A^3"
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2009-07-03 00:38:31 +08:00
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</PRE>
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</HTML>
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