"""The basic equations for the IISPH formulation of
M. Ihmsen, J. Cornelis, B. Solenthaler, C. Horvath, M. Teschner, "Implicit
Incompressible SPH," IEEE Transactions on Visualization and Computer
Graphics, vol. 20, no. 3, pp. 426-435, March 2014.
http://dx.doi.org/10.1109/TVCG.2013.105
"""
from numpy import sqrt
from pysph.sph.equation import Equation
from pysph.sph.integrator_step import IntegratorStep
from pysph.base.reduce_array import serial_reduce_array, parallel_reduce_array
[docs]class IISPHStep(IntegratorStep):
"""A straightforward and simple integrator to be used for IISPH.
"""
[docs] def initialize(self):
pass
[docs] def stage1(self, d_idx, d_x, d_y, d_z, d_u, d_v, d_w,
d_uadv, d_vadv, d_wadv, d_au, d_av, d_aw,
d_ax, d_ay, d_az, dt):
d_u[d_idx] = d_uadv[d_idx] + dt * d_au[d_idx]
d_v[d_idx] = d_vadv[d_idx] + dt * d_av[d_idx]
d_w[d_idx] = d_wadv[d_idx] + dt * d_aw[d_idx]
d_x[d_idx] += dt * d_u[d_idx]
d_y[d_idx] += dt * d_v[d_idx]
d_z[d_idx] += dt * d_w[d_idx]
[docs]class NumberDensity(Equation):
[docs] def initialize(self, d_idx, d_V):
d_V[d_idx] = 0.0
[docs] def loop(self, d_idx, d_V, WIJ):
d_V[d_idx] += WIJ
[docs]class SummationDensity(Equation):
[docs] def initialize(self, d_idx, d_rho):
d_rho[d_idx] = 0.0
[docs] def loop(self, d_idx, d_rho, s_idx, s_m, WIJ):
d_rho[d_idx] += s_m[s_idx]*WIJ
[docs]class SummationDensityBoundary(Equation):
def __init__(self, dest, sources=None, rho0=1.0):
self.rho0 = rho0
super(SummationDensityBoundary, self).__init__(dest, sources)
[docs] def loop(self, d_idx, d_rho, s_idx, s_V, WIJ):
d_rho[d_idx] += self.rho0/s_V[s_idx]*WIJ
[docs]class NormalizedSummationDensity(Equation):
[docs] def initialize(self, d_idx, d_rho, d_rho_adv, d_rho0, d_V):
d_rho0[d_idx] = d_rho[d_idx]
d_rho[d_idx] = 0.0
d_rho_adv[d_idx] = 0.0
d_V[d_idx] = 0.0
[docs] def loop(self, d_idx, d_rho, d_rho_adv, d_V, s_idx, s_m, s_rho0, WIJ):
tmp = s_m[s_idx]*WIJ
d_rho[d_idx] += tmp
d_rho_adv[d_idx] += tmp/s_rho0[s_idx]
d_V[d_idx] += WIJ
[docs] def post_loop(self, d_idx, d_rho, d_rho_adv):
d_rho[d_idx] /= d_rho_adv[d_idx]
[docs]class AdvectionAcceleration(Equation):
def __init__(self, dest, sources=None, gx=0.0, gy=0.0, gz=0.0):
self.gx = gx
self.gy = gy
self.gz = gz
super(AdvectionAcceleration, self).__init__(dest, sources)
[docs] def initialize(self, d_idx, d_au, d_av, d_aw, d_uadv, d_vadv, d_wadv):
d_au[d_idx] = self.gx
d_av[d_idx] = self.gy
d_aw[d_idx] = self.gz
d_uadv[d_idx] = 0.0
d_vadv[d_idx] = 0.0
d_wadv[d_idx] = 0.0
[docs] def post_loop(self, d_idx, d_au, d_av, d_aw, d_uadv, d_vadv, d_wadv,
d_u, d_v, d_w, dt=0.0):
d_uadv[d_idx] = d_u[d_idx] + dt*d_au[d_idx]
d_vadv[d_idx] = d_v[d_idx] + dt*d_av[d_idx]
d_wadv[d_idx] = d_w[d_idx] + dt*d_aw[d_idx]
[docs]class ViscosityAcceleration(Equation):
def __init__(self, dest, sources=None, nu=1.0):
self.nu = nu
super(ViscosityAcceleration, self).__init__(dest, sources)
[docs] def loop(self, d_idx, d_au, d_av, d_aw, s_idx, s_m, EPS,
VIJ, XIJ, RHOIJ1, R2IJ, DWIJ):
dwijdotxij = DWIJ[0]*XIJ[0] + DWIJ[1]*XIJ[1] + DWIJ[2]*XIJ[2]
fac = 2.0*self.nu*s_m[s_idx]*RHOIJ1*dwijdotxij/(R2IJ + EPS)
d_au[d_idx] += fac*VIJ[0]
d_av[d_idx] += fac*VIJ[1]
d_aw[d_idx] += fac*VIJ[2]
[docs]class ViscosityAccelerationBoundary(Equation):
"""The acceleration on the fluid due to a boundary.
"""
def __init__(self, dest, sources=None, rho0=1.0, nu=1.0):
self.nu = nu
self.rho0 = rho0
super(ViscosityAccelerationBoundary, self).__init__(dest, sources)
[docs] def loop(self, d_idx, d_au, d_av, d_aw, d_rho, s_idx, s_V, EPS,
VIJ, XIJ, R2IJ, DWIJ):
phi_b = self.rho0/(s_V[s_idx]*d_rho[d_idx])
dwijdotxij = DWIJ[0]*XIJ[0] + DWIJ[1]*XIJ[1] + DWIJ[2]*XIJ[2]
fac = 2.0*self.nu*phi_b*dwijdotxij/(R2IJ + EPS)
d_au[d_idx] += fac*VIJ[0]
d_av[d_idx] += fac*VIJ[1]
d_aw[d_idx] += fac*VIJ[2]
[docs]class ComputeDII(Equation):
[docs] def initialize(self, d_idx, d_dii0, d_dii1, d_dii2):
d_dii0[d_idx] = 0.0
d_dii1[d_idx] = 0.0
d_dii2[d_idx] = 0.0
[docs] def loop(self, d_idx, d_rho, d_dii0, d_dii1, d_dii2,
s_idx, s_m, DWIJ, dt=0.0):
rho_1 = 1.0/d_rho[d_idx]
fac = -dt*dt*s_m[s_idx]*rho_1*rho_1
d_dii0[d_idx] += fac*DWIJ[0]
d_dii1[d_idx] += fac*DWIJ[1]
d_dii2[d_idx] += fac*DWIJ[2]
[docs]class ComputeDIIBoundary(Equation):
def __init__(self, dest, sources=None, rho0=1.0):
self.rho0 = rho0
super(ComputeDIIBoundary, self).__init__(dest, sources)
[docs] def loop(self, d_idx, d_dii0, d_dii1, d_dii2, d_rho,
s_idx, s_m, s_V, DWIJ, dt=0.0):
rhoi1 = 1.0/d_rho[d_idx]
fac = -dt*dt*rhoi1*rhoi1*self.rho0/s_V[s_idx]
d_dii0[d_idx] += fac*DWIJ[0]
d_dii1[d_idx] += fac*DWIJ[1]
d_dii2[d_idx] += fac*DWIJ[2]
[docs]class ComputeRhoAdvection(Equation):
[docs] def initialize(self, d_idx, d_rho_adv, d_rho, d_p0, d_p, d_piter, d_aii):
d_rho_adv[d_idx] = d_rho[d_idx]
d_p0[d_idx] = d_p[d_idx]
d_piter[d_idx] = 0.5*d_p[d_idx]
[docs] def loop(self, d_idx, d_rho, d_rho_adv, d_uadv, d_vadv, d_wadv, d_u, d_v, d_w,
s_idx, s_m, s_uadv, s_vadv, s_wadv, DWIJ, dt=0.0):
vijdotdwij = (d_uadv[d_idx] - s_uadv[s_idx])*DWIJ[0] + \
(d_vadv[d_idx] - s_vadv[s_idx])*DWIJ[1] + \
(d_wadv[d_idx] - s_wadv[s_idx])*DWIJ[2]
d_rho_adv[d_idx] += dt*s_m[s_idx]*vijdotdwij
[docs]class ComputeRhoBoundary(Equation):
def __init__(self, dest, sources=None, rho0=1.0):
self.rho0 = rho0
super(ComputeRhoBoundary, self).__init__(dest, sources)
[docs] def loop(self, d_idx, d_rho, d_rho_adv, d_uadv, d_vadv, d_wadv,
s_idx, s_u, s_v, s_w, s_V, WIJ, DWIJ, dt=0.0):
phi_b = self.rho0/s_V[s_idx]
vijdotdwij = (d_uadv[d_idx] - s_u[s_idx])*DWIJ[0] + \
(d_vadv[d_idx] - s_v[s_idx])*DWIJ[1] + \
(d_wadv[d_idx] - s_w[s_idx])*DWIJ[2]
d_rho_adv[d_idx] += dt*phi_b*vijdotdwij
[docs]class ComputeAII(Equation):
[docs] def initialize(self, d_idx, d_aii):
d_aii[d_idx] = 0.0
[docs] def loop(self, d_idx, d_aii, d_dii0, d_dii1, d_dii2, d_m, d_rho,
s_idx, s_m, s_rho, DWIJ, dt=0.0):
rho1 = 1.0/d_rho[d_idx]
fac = dt*dt*d_m[d_idx]*rho1*rho1
# The following is m_j (d_ii - d_ji) . DWIJ
# DWIJ = -DWJI
dijdotdwij = (d_dii0[d_idx] - fac*DWIJ[0])*DWIJ[0] + \
(d_dii1[d_idx] - fac*DWIJ[1])*DWIJ[1] + \
(d_dii2[d_idx] - fac*DWIJ[2])*DWIJ[2]
d_aii[d_idx] += s_m[s_idx]*dijdotdwij
[docs]class ComputeAIIBoundary(Equation):
""" This is important and not really discussed in the original IISPH paper.
"""
def __init__(self, dest, sources=None, rho0=1.0):
self.rho0 = rho0
super(ComputeAIIBoundary, self).__init__(dest, sources)
[docs] def loop(self, d_idx, d_aii, d_dii0, d_dii1, d_dii2, d_rho,
s_idx, s_m, s_V, DWIJ, dt=0.0):
phi_b = self.rho0/s_V[s_idx]
dijdotdwij = d_dii0[d_idx]*DWIJ[0] + d_dii1[d_idx]*DWIJ[1] + \
d_dii2[d_idx]*DWIJ[2]
d_aii[d_idx] += phi_b*dijdotdwij
[docs]class ComputeDIJPJ(Equation):
[docs] def initialize(self, d_idx, d_dijpj0, d_dijpj1, d_dijpj2):
d_dijpj0[d_idx] = 0.0
d_dijpj1[d_idx] = 0.0
d_dijpj2[d_idx] = 0.0
[docs] def loop(self, d_idx, d_dijpj0, d_dijpj1, d_dijpj2,
s_idx, s_m, s_rho, s_piter, DWIJ, dt=0.0):
rho1 = 1.0/s_rho[s_idx]
fac = -dt*dt*s_m[s_idx]*rho1*rho1*s_piter[s_idx]
d_dijpj0[d_idx] += fac*DWIJ[0]
d_dijpj1[d_idx] += fac*DWIJ[1]
d_dijpj2[d_idx] += fac*DWIJ[2]
[docs]class PressureSolve(Equation):
def __init__(self, dest, sources=None, rho0=1.0, omega=0.5,
tolerance=1e-2, debug=False):
self.rho0 = rho0
self.omega = omega
self.compression = 0.0
self.debug = debug
self.tolerance = tolerance
super(PressureSolve, self).__init__(dest, sources)
[docs] def initialize(self, d_idx, d_p, d_compression):
d_p[d_idx] = 0.0
d_compression[d_idx] = 0.0
[docs] def loop(self, d_idx, d_p, d_piter, d_rho, d_m, d_dijpj0, d_dijpj1, d_dijpj2,
s_idx, s_m, s_dii0, s_dii1, s_dii2,
s_piter, s_dijpj0, s_dijpj1, s_dijpj2, DWIJ, dt=0.0):
# Note that a good way to check this is to see that when
# d_idx == s_idx the contribution is zero, as is expected.
rho1 = 1.0/d_rho[d_idx]
fac = dt*dt*d_m[d_idx]*rho1*rho1*d_piter[d_idx]
djkpk0 = s_dijpj0[s_idx] - fac*DWIJ[0]
djkpk1 = s_dijpj1[s_idx] - fac*DWIJ[1]
djkpk2 = s_dijpj2[s_idx] - fac*DWIJ[2]
tmp0 = d_dijpj0[d_idx] - s_dii0[s_idx]*s_piter[s_idx] - djkpk0
tmp1 = d_dijpj1[d_idx] - s_dii1[s_idx]*s_piter[s_idx] - djkpk1
tmp2 = d_dijpj2[d_idx] - s_dii2[s_idx]*s_piter[s_idx] - djkpk2
tmpdotdwij = tmp0*DWIJ[0] + tmp1*DWIJ[1] + tmp2*DWIJ[2]
# This is corrected in the post_loop.
d_p[d_idx] += s_m[s_idx]*tmpdotdwij
[docs] def post_loop(self, d_idx, d_piter, d_p0, d_p, d_aii, d_rho_adv, d_rho,
d_compression, dt=0.0):
#tmp = d_rho[d_idx] - d_rho_adv[d_idx] - d_p[d_idx]
tmp = self.rho0 - d_rho_adv[d_idx] - d_p[d_idx]
p = (1.0 - self.omega)*d_piter[d_idx] + self.omega/d_aii[d_idx]*tmp
aii_min = dt*dt*0.01
# Clamp pressure to positive values.
if p < 0.0:
p = 0.0
elif abs(d_aii[d_idx]) < aii_min :
p = 0.0
else:
d_compression[d_idx] = abs(p*d_aii[d_idx] - tmp)
d_piter[d_idx] = p
d_p[d_idx] = p
[docs] def reduce(self, dst):
dst.tmp_comp[0] = serial_reduce_array(dst.array.compression > 0.0, 'sum')
dst.tmp_comp[1] = serial_reduce_array(dst.array.compression, 'sum')
dst.tmp_comp.set_data(parallel_reduce_array(dst.tmp_comp, 'sum'))
if dst.tmp_comp[0] > 0:
comp = dst.tmp_comp[1]/dst.tmp_comp[0]/self.rho0
else:
comp = 0.0
self.compression = comp
[docs] def converged(self):
debug = self.debug
compression = self.compression
if compression > self.tolerance:
if debug:
print("Not converged:", compression)
return -1.0
else:
if debug:
print("Converged:", compression)
return 1.0
[docs]class PressureSolveBoundary(Equation):
def __init__(self, dest, sources=None, rho0=1.0):
self.rho0 = rho0
super(PressureSolveBoundary, self).__init__(dest, sources)
[docs] def loop(self, d_idx, d_p, d_rho, d_dijpj0, d_dijpj1, d_dijpj2,
s_idx, s_V, DWIJ):
phi_b = self.rho0/s_V[s_idx]
dijdotwij = d_dijpj0[d_idx]*DWIJ[0] + \
d_dijpj1[d_idx]*DWIJ[1] + \
d_dijpj2[d_idx]*DWIJ[2]
d_p[d_idx] += phi_b*dijdotwij
[docs]class PressureForce(Equation):
[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, d_rho, d_p, d_au, d_av, d_aw,
s_idx, s_m, s_rho, s_p, DWIJ):
rhoi1 = 1.0/d_rho[d_idx]
rhoj1 = 1.0/s_rho[s_idx]
fac = -s_m[s_idx]*(d_p[d_idx]*rhoi1*rhoi1 + s_p[s_idx]*rhoj1*rhoj1)
d_au[d_idx] += fac*DWIJ[0]
d_av[d_idx] += fac*DWIJ[1]
d_aw[d_idx] += fac*DWIJ[2]
[docs] def post_loop(self, d_idx, d_au, d_av, d_aw,
d_uadv, d_vadv, d_wadv, DT_ADAPT):
fac = d_au[d_idx]*d_au[d_idx] + d_av[d_idx]*d_av[d_idx] +\
d_aw[d_idx]*d_aw[d_idx]
vmag = sqrt(d_uadv[d_idx]*d_uadv[d_idx] + d_vadv[d_idx]*d_vadv[d_idx] +
d_wadv[d_idx]*d_wadv[d_idx])
DT_ADAPT[0] = max(2.0*vmag, DT_ADAPT[0])
DT_ADAPT[1] = max(2.0*fac, DT_ADAPT[1])
[docs]class PressureForceBoundary(Equation):
def __init__(self, dest, sources=None, rho0=1.0):
self.rho0 = rho0
super(PressureForceBoundary, self).__init__(dest, sources)
[docs] def loop(self, d_idx, d_rho, d_au, d_av, d_aw, d_p, s_idx, s_V, DWIJ):
rho1 = 1.0/d_rho[d_idx]
fac = -d_p[d_idx]*rho1*rho1*self.rho0/s_V[s_idx]
d_au[d_idx] += fac*DWIJ[0]
d_av[d_idx] += fac*DWIJ[1]
d_aw[d_idx] += fac*DWIJ[2]