"LIGGGHTS(R)-PUBLIC WWW Site"_liws - "LIGGGHTS(R)-PUBLIC Documentation"_ld - "LIGGGHTS(R)-PUBLIC Commands"_lc :c

:link(liws,http://www.cfdem.com)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)

:line

pair_style sph/artVisc/tensCorr command :h3

[Syntax:]

pair_style sph/artVisc/tensCorr kernelstyle args keyword values ... :pre

sph/artVisc/tensCorr = name of this pair_style command
kernelstyle = {cubicspline} or {wendland}
args = list of arguments for a particular style :ul
  {cubicspline} or {wendland} args = h
    h = smoothing length :pre
zero or more keyword/value pairs may be appended to args
keyword = {artVisc} or {tensCorr} :ul
  {artVisc} values = alpha beta eta
    alpha = free parameter to control shear viscosity
    beta = free parameter to control bulk viscosity
    eta = coefficient to avoid singularities
  {tensCorr} values = epsilon deltap
    epsilon = free parameter
    deltap = initial particle distribution :pre

[Examples:]

pair_style sph/artVisc/tensCorr wendland 0.001 artVisc 1e-4 0 1e-8
pair_style sph/artVisc/tensCorr cubicspline 0.001 artVisc 1e-4 0 1e-8 tensCorr 0.2 1e-2 :pre



[Description:]

The {sph/artVisc/tensCorr} style uses the smoothed particle hydrodynamics (SPH) method according to Monaghan "(1992)"_#Monaghan1992. The acting force is calculated from the acceleration as stated in the equation:

:c,image(Eqs/pair_sph_artvisc_tenscorr_eq1.jpg)

Whereas the indices a and b stand for particles, P<sub>j</sub> stands for pressure and &#961;<sub>j</sub> for the density. W<sub>ab</sub> represents the kernel, which is defined by the kernelstyle.

For kernelstyle cubicspline a piecewise defined, 3-order kernel is used:

:c,image(Eqs/pair_sph_artvisc_tenscorr_eq2.jpg)

The wendland kernel (Wendland,1995) is defined as

:c,image(Eqs/pair_sph_artvisc_tenscorr_eq3.jpg)

The smoothing length h is the most important parameter for SPH-calculations. It depends on initial particle spacing, initial density &#961;<sub>0</sub> and mass per particle m<sub>j</sub>. In case that the smoothing length is about 1.2 times the initial particle spacing and it is a 3-dimensional cubic lattice (therefore the summation is over 57 particles), you can use the following equation "(Liu and Liu, 2003, p. 211-213)"_#LiuLiu2003:

:c,image(Eqs/pair_sph_artvisc_tenscorr_eq4.jpg)

The atom style {sph/var} uses the input argument h as initial smoothing length for all particles. In case the atom style {sph} (per-type smoothing length) is used an additional per-type property {sl} must be defined, e.g.,

fix           m2 all property/global sl peratomtype 0.0012 :pre

For further details on the basics of the SPH-method we recommend the papers from Monaghan "(1992)"_#Monaghan1992, "(1994)"_#Monaghan1994, etc.

Optionally, this pairstyle can take into account the artificial viscosity proposed my Monaghan (1985), if the artVisc keyword is appended. In this case, &#928;<sub>ab</sub> is added to the bracket term in the above acceleration equation, where &#928;<sub>ab</sub> is given by

:c,image(Eqs/pair_sph_artvisc_tenscorr_eq5.jpg)

and

:c,image(Eqs/pair_sph_artvisc_tenscorr_eq6.jpg)

This expression produces a shear and bulk viscosity. The quadratic term enables simulation of high Mach number shocks. The parameter &#951;<sup>2</sup> prevents singularities. A good choice is normally &#951;<sup>2</sup>=0.01h<sup>2</sup>. :b
The choice of &#945; and &#946; should not be critical, although there are some aspects which you should take into account:

  "In the present case, with negligible changes in the density \[weakly compressible SPH\], the viscosity is almost entirely shear viscosity with a viscosity coefficient approximately &#945;hc." "(Monaghan, 1994)"_#Monaghan1994 :p

Bar-parameters like c<sub>ab</sub> and &#961;<sub>ab</sub> are mean values of particle a and b.
NOTE: &#961;<sub>ab</sub> is calculated, and for the calculation of c<sub>ab</sub> the per-type property {speedOfSound} has to be defined, e.g.,

fix 		      m1 all property/global speedOfSound peratomtype 20. :pre

By appending the keyword {tensCorr} you enable the tensile correction algorithm "(Monaghan, 2000)"_#Monaghan2000 which improves results in combination with negative pressures (e.g. EOS like Tait's equation). This method adds R*(f<sub>ab</sub>)<sup>n</sup> to the bracket term, where the factor R is related to the pressure and can be calculated by R=R<sub>a</sub> + R<sub>b</sub>. In case of negative pressures (P<sub>a</sub> < 0) we use the rule

:c,image(Eqs/pair_sph_artvisc_tenscorr_eq7.jpg)

otherwise R<sub>a</sub> is zero. Typical values of {epsilon} are about 0.2.
fab is calculated by

:c,image(Eqs/pair_sph_artvisc_tenscorr_eq8.jpg)

where &Delta;p denotes the initial particle spacing.
NOTE: In a next version this calculation should be improved too.

:line

[Mixing, shift, table, tail correction, restart, rRESPA info]:

The "pair_modify"_pair_modify.html mix, shift, table, and tail options
are not relevant for sph pair styles.

These pair styles write their information to "binary restart
files"_restart.html, so a pair_style command does not need to be
specified in an input script that reads a restart file.

These pair styles can only be used via the {pair} keyword of the
"run_style respa"_run_style.html command.  They do not support the
{inner}, {middle}, {outer} keywords.

:line

[Restrictions:]

...

[Related commands:]

"pair_coeff"_pair_coeff.html

[Default:] none

:line

:link(LiuLiu2003)
[(Liu and Liu, 2003)] "Smoothed Particle Hydrodynamics: A Meshfree Particle Method", G. R. Liu and M. B. Liu, World Scientific, p. 449 (2003).

:link(Monaghan1992)
[(Monaghan, 1992)] "Smoothed Particle Hydrodynamics", J. J. Monaghan, Annu. Rev. Astron. Astrophys., 30, p. 543-574 (1992).

:link(Monaghan1994)
[(Monaghan, 1994)] J. J. Monaghan, Journal of Computational Physics, 110, p. 399-406 (1994).

:link(Monaghan2000)
[(Monaghan, 2000)] J. J. Monaghan, Journal of Computational Physics, 159, p. 290-311 (2000).

