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<HTML>
<CENTER><A HREF = "http://www.cfdem.com">LIGGGHTS WWW Site</A> - <A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LIGGGHTS Documentation</A> - <A HREF = "Section_commands.html#comm">LIGGGHTS Commands</A>
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<HR>
<H3>fix sph/density/continuity command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>fix ID group-ID sph/density/continuity
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
<LI>sph/density/continuity = style name of this fix command
</UL>
<P><B>Examples:</B>
</P>
<PRE>fix density all sph/density/continuity
</PRE>
<P><B>LIGGGHTS vs. LAMMPS Info:</B>
</P>
<P>This command is not available in LAMMPS.
</P>
<P><B>Description:</B>
</P>
<P>Based on the continuity equation in the form
</P>
<CENTER><IMG SRC = "Eqs/fix_sph_density_continuity_eq1.jpg">
</CENTER>
<P>this fix calculates the density of each particle by the rule
</P>
<CENTER><IMG SRC = "Eqs/fix_sph_density_continuity_eq2.jpg">
</CENTER>
<P>where the summation is over all particles b other than particle a, m is the mass, v is the velocity, W<sub>ab</sub> is the interpolating kernel (documented in <A HREF = "pair_sph_artvisc_tenscorr.html">pair_style sph/artVisc/tensCorr</A>) and ∇<sub>a</sub> is the gradient of W<sub>ab</sub>.
</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>.
</P>
<P>None of the <A HREF = "fix_modify.html">fix_modify</A> options are relevant to this fix.
</P>
<P>No global scalar or vector or per_atom quantities are stored by this fix for access by various <A HREF = "Section_howto.html#4_15">output commands</A>.
</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.
</P>
<P>This fix is not invoked during <A HREF = "minimize.html">energy minimization</A>.
</P>
<HR>
<P><B>Restrictions:</B>
</P>
<P>There can be only one fix sph/density.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "pair_sph_artvisc_tenscorr.html">pair_style sph/artVisc/tensCorr</A>, <A HREF = "fix_sph_pressure.html">fix sph/pressure</A>, <A HREF = "fix_sph_density_corr.html">fix sph/density/corr</A>
</P>
<P><B>Default:</B> none
</P>
<HR>
<A NAME = "LiuLiu2003"></A>
<P><B>(Liu and Liu, 2003)</B> "Smoothed Particle Hydrodynamics: A Meshfree Particle Method", G. R. Liu and M. B. Liu, World Scientific, p. 449 (2003).
</P>
<A NAME = "Monaghan1992"></A>
<P><B>(Monaghan, 1992)</B> "Smoothed Particle Hydrodynamics", J. J. Monaghan, Annu. Rev. Astron. Astrophys., 30, p. 543-574 (1992).
</P>
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