"""Viscosity functions"""
from pysph.sph.equation import Equation
[docs]class LaminarViscosity(Equation):
def __init__(self, dest, sources=None, nu=1e-6, eta=0.01):
self.nu = nu
self.eta = eta
super(LaminarViscosity,self).__init__(dest, sources)
[docs] def loop(self, d_idx, s_idx, s_m, d_rho, s_rho,
d_au, d_av, d_aw, DWIJ, XIJ, VIJ, R2IJ, HIJ):
rhoa = d_rho[d_idx]
rhob = s_rho[s_idx]
# scalar part of the kernel gradient
Fij = DWIJ[0] * XIJ[0] + DWIJ[1] * XIJ[1] + DWIJ[2] * XIJ[2]
mb = s_m[s_idx]
tmp = mb * 4 * self.nu * Fij/( (rhoa + rhob)*(R2IJ + self.eta*HIJ*HIJ) )
# accelerations
d_au[d_idx] += tmp * VIJ[0]
d_av[d_idx] += tmp * VIJ[1]
d_aw[d_idx] += tmp * VIJ[2]
[docs]class MonaghanSignalViscosityFluids(Equation):
def __init__(self, dest, sources=None, alpha=0.5, h=None):
self.alpha=0.125 * alpha * h
if h is None:
raise ValueError("Invalid value for parameter h : %s"%h)
super(MonaghanSignalViscosityFluids,self).__init__(dest, sources)
[docs] def loop(self, d_idx, s_idx, d_rho, s_rho, s_m,
d_au, d_av, d_aw, d_cs, s_cs,
RIJ, HIJ, VIJ, XIJ, DWIJ):
nua = self.alpha * d_cs[d_idx]
nub = self.alpha * s_cs[s_idx]
rhoa = d_rho[d_idx]
rhob = s_rho[s_idx]
mb = s_m[s_idx]
vabdotrab = VIJ[0]*XIJ[0] + VIJ[1]*XIJ[1] + VIJ[2]*XIJ[2]
force = -16 * nua * nub/(nua*rhoa + nub*rhob) * vabdotrab/(HIJ * (RIJ + 0.01*HIJ*HIJ))
d_au[d_idx] += -mb * force * DWIJ[0]
d_av[d_idx] += -mb * force * DWIJ[1]
d_aw[d_idx] += -mb * force * DWIJ[2]
[docs]class ClearyArtificialViscosity(Equation):
"""Artificial viscosity proposed By P. Cleary:
.. math::
\mathcal{Pi}_{ab} = -\frac{16}{\mu_a \mu_b}{\rho_a \rho_b
(\mu_a + \mu_b)}\left( \frac{\boldsymbol{v}_{ab} \cdot
\boldsymbol{r}_{ab}}{\boldsymbol{r}_{ab}^2 + \epsilon} \right),
where the viscosity is determined from the parameter
:math:`\alpha` as
.. math::
\mu_a = \frac{1}{8}\alpha h_a c_a \rho_a
This equation is described in the 2005 review paper by Monaghan
- J. J. Monaghan, "Smoothed Particle Hydrodynamics", Reports on
Progress in Physics, 2005, 68, pp 1703--1759 [JM05]
"""
def __init__(self, dest, sources, alpha=1.0, dim=2):
self.alpha = alpha
self.factor = 16.0
if dim == 3:
self.factor = 20.0
# Base class initialization
super(ClearyArtificialViscosity, self).__init__(dest, sources)
[docs] def initialize(self, d_idx, d_au, d_av, d_aw):
d_au[d_idx] = 0.0
d_av[d_idx] = 0.0
d_aw[d_idx] = 0.0
[docs] def loop(self, d_idx, s_idx, d_m, s_m, d_rho, s_rho, d_h, s_h, d_cs, s_cs,
d_au, d_av, d_aw, XIJ, VIJ, R2IJ, EPS, DWIJ):
# viscosity parameters for each particle Eq. (8.8) in [JM05]
mua = 0.125 * self.alpha * d_h[d_idx] * d_cs[d_idx] * d_rho[d_idx]
mub = 0.125 * self.alpha * s_h[s_idx] * s_cs[s_idx] * s_rho[s_idx]
# \boldsymbol{v}_{ab} \cdot \boldsymbol{r}_{ab}
dot = VIJ[0]*XIJ[0] + VIJ[1]*XIJ[1] + VIJ[2]*XIJ[2]
# Pi_ab term. Eq. (8.9) in [JM05]
rhoa = d_rho[d_idx]; rhob = s_rho[s_idx]
piab = -s_m[s_idx] * self.factor*mua*mub/(rhoa*rhob*(mua + mub)) * (dot/(R2IJ + EPS))
# accelerations due to viscosity Eq. (8.2) in [JM05]
d_au[d_idx] += piab * DWIJ[0]
d_av[d_idx] += piab * DWIJ[1]
d_aw[d_idx] += piab * DWIJ[2]