• sph = name of this pair_style command
• kernelstyle = cubicspline or wendland
• args = list of arguments for a particular style

   cubicspline or wendland args = h
      h = smoothing length

• zero or more keyword/value pairs may be appended to args
• keyword = artVisc or tensCorr

    artVisc values = alpha beta cAB eta
      alpha = free parameter to control shear viscosity
      beta = free parameter to control bulk viscosity
      cAB = average speed of sound (velocity units)
      eta = coefficient to avoid singularities
    tensCorr values = epsilon
      epsilon = free parameter 

Examples:

pair_style sph wendland 0.001 artVisc 1e-4 0 1484. 1e-8
pair_style sph cubicspline 0.001 artVisc 1e-4 0 480 1e-8 tensCorr 0.2

LIGGGHTS vs. LAMMPS Info:

This command is not available in LAMMPS.

Description:

The sph style use the smoothed particle hydrodynamics (SPH) method according to Monaghan: "Smoothed Particle Hydrodynamics", J. J. Monaghan, Annual Review of Astronomy and Astrophysics (1992), Volume 30, Pages 543-574. The acting force is calculated from the acceleration as stated in the equation:

Whereas the indices a and b stand for particles, P_j stands for pressure and ρ_j for the density. W_ab represents the kernel, which is defined by the kernelstyle.

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

The wendland kernel (Wendland,1995) is defined as

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 m_j. 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):

For further details on the basics of the SPH-method we recommend the papers from Monaghan 1992,1994, etc.

Optionally, this pairstyle can take into account the artificial viscosity proposed my Monaghan (1985), if the artVisc keyword is appended. In this case, Π_ab is added to the bracket term in the above acceleration equation, where Π_ab is given by

and

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.
The choice of α and β should not be critical, although there are some aspects which you should take into account:

  In case of negligible changes in the density (weakly compressible SPH) it is almost only shear viscosity with a viscosity coefficient approximately αhc. (Monaghan, 1994)

Bar-parameters like c_ab and ρ_ab are mean values of particle a and b.
NOTE: ρ_ab is calculated, whereas c_ab is a given parameter. In a next version speed of sound should be added as atom property.

By appending the keyword tensCorr you enable the tensile correction algorithm (Monaghan, 2000) which improves results in combination with negative pressures (e.g. EOS like Tait's equation). This method adds R*(f_ab)ⁿ to the bracket term, where the factor R is related to the pressure and can be calculated by R=R_a + R_b. In case of negative pressures (P_a < 0) we use the rule

otherwise R_a is zero. Typical values of epsilon are about 0.2.
f_ab is calculated by

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

Restart info:

Until now there is no restart option implemented.

Restrictions:

...

Related commands:

pair_coeff

Default: none

(Monaghan1992) J. J. Monaghan, Annu. Rev. Astron. Astrophys., 30, p. 543-574 (1992).

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

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