/usr/lib/python2.7/dist-packages/PySPH-1.0a4.dev0-py2.7-linux-x86_64.egg/pysph/sph/gas_dynamics/basic.py is in python-pysph 0~20160514.git91867dc-4build1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 | """Basic equations for Gas-dynamics"""
from pysph.sph.equation import Equation
from math import sqrt
class ScaleSmoothingLength(Equation):
def __init__(self, dest, sources, factor=2.0):
super(ScaleSmoothingLength, self).__init__(dest, sources)
self.factor = factor
def loop(self, d_idx, d_h):
d_h[d_idx] = d_h[d_idx] * self.factor
class UpdateSmoothingLengthFromVolume(Equation):
def __init__(self, dest, sources, dim, k=1.2):
super(UpdateSmoothingLengthFromVolume, self).__init__(dest, sources)
self.k = k
self.dim1 = 1./dim
def loop(self, d_idx, d_m, d_rho, d_h):
d_h[d_idx] = self.k * pow( d_m[d_idx]/d_rho[d_idx], self.dim1)
class SummationDensity(Equation):
def __init__(
self, dest, sources, dim,
density_iterations=False, iterate_only_once=False, k=1.2, htol=1e-6):
r"""Summation density with iterative solution of the smoothing lengths.
Parameters:
density_iterations : bint
Flag to indicate density iterations are required.
iterate_only_once : bint
Flag to indicate if only one iteration is required
k : double
Kernel scaling factor
htol : double
Iteration tolerance
"""
self.density_iterations = density_iterations
self.iterate_only_once = iterate_only_once
self.dim = dim
self.k = k
self.htol = htol
# by default, we set the equation_has_converged attribute to True. If
# density_iterations is set to True, we will have at least one
# iteration to determine the new smoothing lengths since the
# 'converged' property of the particles is intialized to False
self.equation_has_converged = 1
super(SummationDensity, self).__init__(dest, sources)
def initialize(
self, d_idx, d_rho, d_div, d_grhox, d_grhoy, d_arho, d_dwdh):
d_rho[d_idx] = 0.0
d_div[d_idx] = 0.0
d_grhox[d_idx] = 0.0
d_grhoy[d_idx] = 0.0
d_arho[d_idx] = 0.0
d_dwdh[d_idx] = 0.0
# set the converged attribute for the Equation to True. Within
# the post-loop, if any particle hasn't converged, this is set
# to False. The Group can therefore iterate till convergence.
self.equation_has_converged = 1
def loop(self, d_idx, s_idx, d_rho, d_grhox, d_grhoy, d_arho,
d_dwdh, s_m, d_converged, VIJ, WI, DWI, GHI):
mj = s_m[s_idx]
vijdotdwij = VIJ[0]*DWI[0] + VIJ[1]*DWI[1] + VIJ[2]*DWI[2]
# density
d_rho[d_idx] += mj * WI
# density accelerations
d_arho[d_idx] += mj * vijdotdwij
# gradient of density
d_grhox[d_idx] += mj * DWI[0]
d_grhoy[d_idx] += mj * DWI[1]
# gradient of kernel w.r.t h
d_dwdh[d_idx] += mj * GHI
def post_loop(self, d_idx, d_arho, d_rho, d_div, d_omega, d_dwdh,
d_h0, d_h, d_m, d_ah, d_converged):
# iteratively find smoothing length consistent with the
if self.density_iterations:
if not ( d_converged[d_idx] == 1 ):
# current mass and smoothing length. The initial
# smoothing length h0 for this particle must be set
# outside the Group (that is, in the integrator)
mi = d_m[d_idx]; hi = d_h[d_idx]; hi0 = d_h0[d_idx]
# density from the mass, smoothing length and kernel
# scale factor
rhoi = mi/(hi/self.k)**self.dim
dhdrhoi = -hi/( self.dim*d_rho[d_idx] )
dwdhi = d_dwdh[d_idx]
omegai = 1.0 - dhdrhoi*dwdhi
# correct omegai
if omegai < 0:
omegai = 1.0
# kernel multiplier. These are the multiplicative
# pre-factors, or the "grah-h" terms in the
# equations. Remember that the equations use 1/omega
gradhi = 1.0/omegai
d_omega[d_idx] = gradhi
# the non-linear function and it's derivative
func = rhoi - d_rho[d_idx]
dfdh = omegai/dhdrhoi
# Newton Raphson estimate for the new h
hnew = hi - func/dfdh
# Nanny control for h
if ( hnew > 1.2 * hi ):
hnew = 1.2 * hi
elif ( hnew < 0.8 * hi ):
hnew = 0.8 * hi
# overwrite if gone awry
if ( (hnew <= 1e-6) or (gradhi < 1e-6) ):
hnew = self.k * (mi/d_rho[d_idx])**(1./self.dim)
# check for convergence
diff = abs( hnew-hi )/hi0
if not ( (diff < self.htol) and (omegai > 0) or self.iterate_only_once):
# this particle hasn't converged. This means the
# entire group must be repeated until this fellow
# has converged, or till the maximum iteration has
# been reached.
self.equation_has_converged = -1
# set particle properties for the next
# iteration. For the 'converged' array, a value of
# 0 indicates the particle hasn't converged
d_h[d_idx] = hnew
d_converged[d_idx] = 0
else:
d_arho[d_idx] *= d_omega[d_idx]
d_ah[d_idx] = d_arho[d_idx] * dhdrhoi
d_converged[d_idx] = 1
# comptue the divergence of velocity
d_div[d_idx] = -d_arho[d_idx]/d_rho[d_idx]
def converged(self):
return self.equation_has_converged
class IdealGasEOS(Equation):
def __init__(self, dest, sources, gamma):
self.gamma = gamma
self.gamma1 = gamma - 1.0
super(IdealGasEOS, self).__init__(dest, sources)
def loop(self, d_idx, d_p, d_rho, d_e, d_cs):
d_p[d_idx] = self.gamma1 * d_rho[d_idx] * d_e[d_idx]
d_cs[d_idx] = sqrt( self.gamma * d_p[d_idx]/d_rho[d_idx] )
class Monaghan92Accelerations(Equation):
def __init__(self, dest, sources, alpha=1.0, beta=2.0):
self.alpha = alpha
self.beta = beta
super(Monaghan92Accelerations, self).__init__(dest, sources)
def initialize(self, d_idx, d_au, d_av, d_aw, d_ae):
d_au[d_idx] = 0.0
d_av[d_idx] = 0.0
d_aw[d_idx] = 0.0
d_ae[d_idx] = 0.0
def loop(self, d_idx, s_idx, d_rho, s_rho, d_p, s_p, d_cs, s_cs,
d_au, d_av, d_aw, d_ae, s_m,
VIJ, DWIJ, XIJ, EPS, HIJ, R2IJ, RHOIJ1):
rhoi2 = d_rho[d_idx] * d_rho[d_idx]
rhoj2 = s_rho[s_idx] * s_rho[s_idx]
tmpi = d_p[d_idx]/rhoi2
tmpj = s_p[s_idx]/rhoj2
vijdotxij = VIJ[0]*XIJ[0] + VIJ[1]*XIJ[1] + VIJ[2]*XIJ[2]
piij = 0.0
if vijdotxij < 0:
muij = HIJ*vijdotxij/(R2IJ + EPS)
cij = 0.5 * (d_cs[d_idx] + s_cs[s_idx])
piij = -self.alpha*cij*muij + self.beta*muij*muij
piij *= RHOIJ1
d_au[d_idx] += -s_m[s_idx] * (tmpi + tmpj + piij) * DWIJ[0]
d_av[d_idx] += -s_m[s_idx] * (tmpi + tmpj + piij) * DWIJ[1]
d_aw[d_idx] += -s_m[s_idx] * (tmpi + tmpj + piij) * DWIJ[2]
vijdotdwij = VIJ[0]*DWIJ[0] + VIJ[1]*DWIJ[1] + VIJ[2]*DWIJ[2]
d_ae[d_idx] += 0.5 * s_m[s_idx] * (tmpi + tmpj + piij) * vijdotdwij
class MPMAccelerations(Equation):
def __init__(
self, dest, sources, beta=2.0,
update_alpha1=False, update_alpha2=False,
alpha1_min=0.1, alpha2_min=0.1, sigma=0.1):
self.beta = beta
self.sigma = sigma
self.update_alpha1 = update_alpha1
self.update_alpha2 = update_alpha2
self.alpha1_min = alpha1_min
self.alpha2_min = alpha2_min
super(MPMAccelerations, self).__init__(dest, sources)
def initialize(self, d_idx, d_au, d_av, d_aw, d_ae, d_am,
d_aalpha1, d_aalpha2, d_del2e):
d_au[d_idx] = 0.0
d_av[d_idx] = 0.0
d_aw[d_idx] = 0.0
d_ae[d_idx] = 0.0
d_aalpha1[d_idx] = 0.0
d_aalpha2[d_idx] = 0.0
d_del2e[d_idx] = 0.0
def loop(self, d_idx, s_idx, d_m, s_m, d_p, s_p, d_cs, s_cs,
d_e, s_e, d_rho, s_rho, d_au, d_av, d_aw, d_ae,
d_omega, s_omega, XIJ, VIJ, DWI, DWJ, DWIJ, HIJ,
d_del2e, d_alpha1, s_alpha1, d_alpha2, s_alpha2,
EPS, RIJ, R2IJ, RHOIJ, DT_ADAPT):
# particle pressure
pi = d_p[d_idx]
pj = s_p[s_idx]
# pi/rhoi**2
rhoi2 = d_rho[d_idx]*d_rho[d_idx]
pibrhoi2 = pi/rhoi2
# pj/rhoj**2
rhoj2 = s_rho[s_idx]*s_rho[s_idx]
pjbrhoj2 = pj/rhoj2
# averaged sound speed
cij = 0.5 * (d_cs[d_idx] + s_cs[s_idx])
# averaged mass
mi = d_m[d_idx]
mj = s_m[s_idx]
mij = 0.5 * (mi + mj)
# averaged sound speed
ci = d_cs[d_idx]
cj = s_cs[s_idx]
cij = 0.5 * (ci + cj)
# normalized interaction vector
if RIJ < 1e-8:
XIJ[0] = 0.0
XIJ[1] = 0.0
XIJ[2] = 0.0
else:
XIJ[0] /= RIJ
XIJ[1] /= RIJ
XIJ[2] /= RIJ
# v_{ij} \cdot r_{ij} or vijdotxij
dot = VIJ[0]*XIJ[0] + VIJ[1]*XIJ[1] + VIJ[2]*XIJ[2]
# scalar part of the kernel gradient DWIJ
Fij = XIJ[0]*DWIJ[0] + XIJ[1]*DWIJ[1] + XIJ[2]*DWIJ[2]
# signal velocities
pdiff = abs(pi-pj)
vsig1 = 0.5 * max(cij - self.beta*dot, 0.0)
vsig2 = sqrt( pdiff/RHOIJ )
# compute the Courant-limited time step factor.
DT_ADAPT[0] = max( DT_ADAPT[0], cij + self.beta * dot )
# Artificial viscosity
if dot <= 0.0:
# viscosity
alpha1 = 0.5 * (d_alpha1[d_idx] + s_alpha1[s_idx])
tmpv = mj/RHOIJ * alpha1 * vsig1 * dot
d_au[d_idx] += tmpv * DWIJ[0]
d_av[d_idx] += tmpv * DWIJ[1]
d_aw[d_idx] += tmpv * DWIJ[2]
# viscous contribution to the thermal energy
d_ae[d_idx] += -0.5*mj/RHOIJ*alpha1*vsig1*dot*dot*Fij
# grad-h correction terms. These will be set to 1.0 by the
# integrator and thus can be used safely.
omegai = d_omega[d_idx]; omegaj = s_omega[s_idx]
# gradient terms
d_au[d_idx] += -mj*(pibrhoi2*omegai*DWI[0] + pjbrhoj2*omegaj*DWJ[0])
d_av[d_idx] += -mj*(pibrhoi2*omegai*DWI[1] + pjbrhoj2*omegaj*DWJ[1])
d_aw[d_idx] += -mj*(pibrhoi2*omegai*DWI[2] + pjbrhoj2*omegaj*DWJ[2])
# accelerations for the thermal energy
vijdotdwi = VIJ[0]*DWI[0] + VIJ[1]*DWI[1] + VIJ[2]*DWI[2]
d_ae[d_idx] += mj * pibrhoi2 * omegai * vijdotdwi
# thermal conduction
alpha2 = 0.5 * (d_alpha2[d_idx] + s_alpha2[s_idx])
eij = d_e[d_idx] - s_e[s_idx]
d_ae[d_idx] += mj/RHOIJ * alpha2 * vsig2 * eij * Fij
# Laplacian of thermal energy
d_del2e[d_idx] += mj/s_rho[s_idx] * eij/(RIJ + EPS) * Fij
def post_loop(self, d_idx, d_h, d_cs, d_alpha1, d_aalpha1, d_div,
d_del2e, d_e, d_alpha2, d_aalpha2):
hi = d_h[d_idx]
tau = hi/(self.sigma*d_cs[d_idx])
if self.update_alpha1:
S1 = max( -d_div[d_idx], 0.0 )
d_aalpha1[d_idx] = (self.alpha1_min - d_alpha1[d_idx])/tau + S1
if self.update_alpha2:
#S2 = d_h[d_idx] * abs(d_del2e[d_idx])/sqrt(d_e[d_idx])
S2 = 0.01 * d_h[d_idx] * d_del2e[d_idx]
d_aalpha2[d_idx] = (self.alpha2_min - d_alpha2[d_idx])/tau + S2
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