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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, Pj stands for pressure and ρj for the density. Wab 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 ρ0 and mass per particle mj. 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, Πab is added to the bracket term in the above acceleration equation, where Πab 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 η2 prevents singularities. A good choice is normally η2=0.01h2. :b
The choice of α and β 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 αhc." "(Monaghan, 1994)"_#Monaghan1994 :p

Bar-parameters like cab and ρab are mean values of particle a and b.
NOTE: ρab is calculated, and for the calculation of cab 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*(fab)n to the bracket term, where the factor R is related to the pressure and can be calculated by R=Ra + Rb. In case of negative pressures (Pa < 0) we use the rule

:c,image(Eqs/pair_sph_artvisc_tenscorr_eq7.jpg)

otherwise Ra is zero. Typical values of {epsilon} are about 0.2.
fab is calculated by

:c,image(Eqs/pair_sph_artvisc_tenscorr_eq8.jpg)

where Δp denotes the initial particle spacing.
NOTE: In a next version this calculation should be improved too.

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[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.

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[Restrictions:]

...

[Related commands:]

"pair_coeff"_pair_coeff.html

[Default:] none

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: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).

