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<HR>
<H3>fix ave/euler command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>fix ID group-ID ave/euler nevery N cell_size_relative c
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
<LI>ave/euler = style name of this fix command
<LI>nevery = obligatory keyword
<LI>n = calculate average values every this many timesteps
<LI>cell_size_relative = obligatory keyword
<LI>c = cell size in multiples of max cutoff
</UL>
<P><B>Examples:</B>
</P>
<PRE>fix 1 all ave/euler nevery 100 cell_size_relative 4.5
</PRE>
<P><B>Description:</B>
</P>
<P>Calculate cell-based averages of velocity, radius, volume fraction,
and pressure (-1/3 * trace of the stress tensor) every few timesteps,
as specified by the <I>nevery</I> keyword. The size of the cells is calculated
as multiple of the maximum cutoff, via the <I>cell_size_relative</I>.
Note that at least a relative cell size of 3 is required.
</P>
<P>Note that velocity is favre (mass) averaged, whereas radius is arithmetically
averaged. To calculate the stress, this command internally uses a
<A HREF = "compute_stress_atom.html">compute stress/atom</A> . It includes the convective
term correctly for granular particles with non-zero average velocity
(which is not included in <A HREF = "compute_stress_atom.html">compute stress/atom</A>).
However, it does not include bond, angle, diahedral or kspace contributions
so that the stress tensor finally reads
</P>
<CENTER><IMG SRC = "Eqs/stress_tensor_granular.png">
</CENTER>
<P>where vave is the (cell-based) average velocity.
The first term is a kinetic energy contribution for atom <I>I</I>. The
second term is a pairwise energy contribution where <I>n</I> loops over the
<I>Np</I> neighbors of atom <I>I</I>, <I>r1</I> and <I>r2</I> are the positions of the 2
atoms in the pairwise interaction, and <I>F1</I> and <I>F2</I> are the forces on
the 2 atoms resulting from the pairwise interaction.
</P>
<HR>
<P><B>Restart, fix_modify, output, run start/stop, minimize info:</B>
</P>
<P>No information about this fix is written to <A HREF = "restart.html">binary restart
files</A>. None of the <A HREF = "fix_modify.html">fix_modify</A> options
are relevant to this fix.
</P>
<P>This fix computes the above-mentioned quantities for output via a
<A HREF = "dump.html">dump euler/vtk</A> command. The values can
only be accessed on timesteps that are multiples of <I>nevery</I> since that
is when calculations are performed.
</P>
<P>No parameter of this fix can be used with the <I>start/stop</I> keywords of
the <A HREF = "run.html">run</A> command. This fix is not invoked during <A HREF = "minimize.html">energy
minimization</A>.
</P>
<P><B>Restrictions:</B>
</P>
<P>Volume fractions and stresses are calculated based on the assumption
of a structured (equidistant regular) grid, so volume fractions and
stresses near walls that are not alligned with the grid will be
incorrect.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "compute.html">compute</A>, <A HREF = "compute_stress_atom.html">compute stress/atom</A>,
<A HREF = "fix_ave_atom.html">fix ave/atom</A>, <A HREF = "fix_ave_histo.html">fix ave/histo</A>,
<A HREF = "fix_ave_time.html">fix ave/time</A>, <A HREF = "fix_ave_spatial.html">fix ave/spatial</A>,
</P>
<P><B>Default:</B> none
</P>
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