def create_equations(self):
equations = [
Group(equations=[
LiuFluidForce(
dest='fluid',
sources=None,
),
XSPHCorrection(dest='fluid', sources=[
'fluid',
]),
TaitEOS(dest='fluid',
sources=None,
rho0=1000,
c0=1498,
gamma=7.0),
],
real=False),
Group(equations=[
ContinuityEquation(dest='fluid', sources=[
'fluid',
]),
MomentumEquation(dest='fluid',
sources=['fluid'],
alpha=0.1,
beta=0.0,
c0=1498,
gy=-9.81),
XSPHCorrection(dest='fluid', sources=['fluid']),
]),
]
return equations
def create_equations(self):
equations = [
Group(equations=[
TaitEOS(dest='fluid', sources=None, rho0=self.ro, c0=self.co,
gamma=7.0),
TaitEOS(dest='tank', sources=None, rho0=self.ro, c0=self.co,
gamma=7.0),
], real=False),
Group(equations=[
ContinuityEquation(
dest='fluid',
sources=['fluid', 'tank', 'cube'],),
ContinuityEquation(
dest='tank',
sources=['fluid', 'tank', 'cube'], ),
MomentumEquation(dest='fluid', sources=['fluid', 'tank'],
alpha=self.alpha, beta=0.0, c0=self.co,
gy=-9.81),
SolidForceOnFluid(dest='fluid', sources=['cube']),
XSPHCorrection(dest='fluid', sources=['fluid', 'tank']),
]),
Group(equations=[
BodyForce(dest='cube', sources=None, gy=-9.81),
FluidForceOnSolid(dest='cube', sources=['fluid']),
# RigidBodyCollision(
# dest='cube',
# sources=['tank'],
# kn=1e5,
# en=0.5, )
]),
Group(equations=[RigidBodyMoments(dest='cube', sources=None)]),
Group(equations=[RigidBodyMotion(dest='cube', sources=None)]),
]
return equations
def create_equations(self):
equations = [
Group(equations=[
TaitEOS(dest='fluid', sources=None, rho0=self.ro, c0=self.co,
gamma=7.0),
TaitEOS(dest='tank', sources=None, rho0=self.ro, c0=self.co,
gamma=7.0),
], real=False),
Group(equations=[
SummationDensityShepardFilter(
dest='fluid',
sources=['fluid', 'tank'], ),
# SummationDensityShepardFilter(
# dest='tank',
# sources=['fluid', 'tank'], ),
SummationDensity(
dest='tank',
sources=['fluid', 'tank'], ),
MomentumEquation(dest='fluid', sources=['fluid', 'tank'],
alpha=self.alpha, beta=0.0, c0=self.co,
gy=-9.81),
XSPHCorrection(dest='fluid', sources=['fluid', 'tank']),
]),
]
return equations
def create_equations(self):
equations = [
Group(equations=[
TaitEOS(dest='fluid',
sources=None,
rho0=1000,
c0=self.co,
gamma=7.0),
TaitEOS(dest='wall',
sources=None,
rho0=1000,
c0=self.co,
gamma=7.0),
],
real=False),
Group(equations=[
ContinuityEquation(dest='fluid', sources=['fluid', 'wall']),
ContinuityEquation(dest='wall', sources=['fluid', 'wall']),
MomentumEquation(dest='fluid',
sources=['fluid', 'wall'],
alpha=self.alpha,
beta=0.0,
c0=self.co,
gy=-9.81),
XSPHCorrection(dest='fluid', sources=['fluid']),
]),
]
return equations
def get_equations(self):
from pysph.sph.basic_equations import XSPHCorrection
from pysph.sph.wc.basic import TaitEOS
from pysph.sph.wc.viscosity import LaminarViscosity
all = self.fluids
equations = []
eq0 = []
for fluid in self.fluids:
eq0.append(CRKSPHPreStep(dest=fluid, sources=all, dim=2))
equations.append(Group(equations=eq0, real=False))
eq1 = []
for fluid in self.fluids:
eq1.append(NumberDensity(dest=fluid, sources=all))
equations.append(Group(equations=eq1, real=False))
eq2 = []
for fluid in self.fluids:
eq2.extend([
CRKSPH(dest=fluid, sources=all, dim=self.dim, tol=self.tol),
SummationDensityCRKSPH(dest=fluid, sources=all)
])
equations.append(Group(equations=eq2, real=False))
eq3 = []
for fluid in self.fluids:
eq3.append(
TaitEOS(dest=fluid, sources=None, rho0=self.rho0, c0=self.c0,
p0=self.p0, gamma=self.gamma))
equations.append(Group(equations=eq3, real=False))
eq4 = []
for fluid in self.fluids:
eq4.extend([
CRKSPH(dest=fluid, sources=all, dim=self.dim, tol=self.tol),
VelocityGradient(dest=fluid, sources=all, dim=self.dim)
])
equations.append(Group(equations=eq4))
eq5 = []
for fluid in self.fluids:
eq5.extend([
CRKSPHSymmetric(dest=fluid, sources=all, dim=self.dim,
tol=self.tol),
MomentumEquation(
dest=fluid, sources=all, dim=self.dim, gx=self.gx,
gy=self.gy, gz=self.gz, cl=self.cl, cq=self.cq,
eta_crit=self.eta_crit, eta_fold=self.eta_fold
),
XSPHCorrection(dest=fluid, sources=all)
])
if abs(self.nu) > 1e-14:
eq5.append(LaminarViscosity(
dest=fluid, sources=self.fluids, nu=self.nu
))
equations.append(Group(equations=eq5))
return equations
def create_equations(self):
"""Set up equations.
Body force is necessary to reset fx,fy,fz, although
not body force is applied.
"""
equations = [
Group(equations=[
BodyForce(dest='ellipsoid', sources=None),
NumberDensity(dest='ellipsoid', sources=['ellipsoid']),
NumberDensity(dest='walls', sources=['walls'])
]),
# Tait equation of state
Group(equations=[
TaitEOS(dest='fluid',
sources=None,
rho0=self.rho,
c0=self.co,
gamma=7.0),
TaitEOSHGCorrection(dest='ellipsoid',
sources=None,
rho0=self.rho,
c0=self.co,
gamma=7.0),
TaitEOSHGCorrection(dest='walls',
sources=None,
rho0=self.rho,
c0=self.co,
gamma=7.0),
],
real=False),
Group(equations=[
ContinuityEquation(dest='fluid',
sources=['fluid', 'walls', 'ellipsoid']),
ContinuityEquation(dest='ellipsoid', sources=['fluid']),
ContinuityEquation(dest='walls', sources=['fluid']),
LaminarViscosity(
dest='fluid', sources=['fluid', 'walls'], nu=self.nu),
MomentumEquation(dest='fluid',
sources=['fluid', 'walls'],
alpha=self.alpha,
beta=0.0,
c0=self.co),
ViscosityRigidBody(dest='fluid',
sources=['ellipsoid'],
nu=self.nu,
rho0=self.rho),
PressureRigidBody(dest='fluid',
sources=['ellipsoid'],
rho0=self.rho),
XSPHCorrection(dest='fluid', sources=['fluid']),
]),
Group(
equations=[RigidBodyMoments(dest='ellipsoid', sources=None)]),
Group(equations=[RigidBodyMotion(dest='ellipsoid', sources=None)]),
]
return equations
def create_equations(self):
equations = [
Group(equations=[
BodyForce(dest='ball', sources=None, gy=gz),
]),
Group(equations=[
TaitEOS(dest='fluid',
sources=None,
rho0=self.ro,
c0=self.co,
gamma=7.0),
TaitEOS(dest='wall',
sources=None,
rho0=self.ro,
c0=self.co,
gamma=7.0),
TaitEOS(dest='temp_wall',
sources=None,
rho0=self.ro,
c0=self.co,
gamma=7.0),
],
real=False),
Group(equations=[
ContinuityEquation(
dest='fluid',
sources=['fluid', 'temp_wall', 'wall'],
),
ContinuityEquation(
dest='temp_wall',
sources=['fluid', 'temp_wall', 'wall'],
),
ContinuityEquation(
dest='wall',
sources=['fluid', 'temp_wall', 'wall'],
),
MomentumEquation(dest='fluid',
sources=['fluid', 'wall', 'temp_wall'],
alpha=self.alpha,
beta=0.0,
c0=self.co,
gy=-9.81),
SolidFluidForce(
dest='fluid',
sources=['ball'],
),
XSPHCorrection(dest='fluid',
sources=['fluid', 'temp_wall', 'wall']),
]),
Group(equations=[
RigidBodyCollision(
dest='ball', sources=['ball', 'wall', 'temp_wall'], kn=1e5)
]),
Group(equations=[RigidBodyMoments(dest='ball', sources=None)]),
Group(equations=[RigidBodyMotion(dest='ball', sources=None)]),
]
return equations
def get_equations(self):
from pysph.sph.equation import Group
from pysph.sph.basic_equations import (ContinuityEquation,
MonaghanArtificialViscosity,
XSPHCorrection,
VelocityGradient2D)
from pysph.sph.solid_mech.basic import (IsothermalEOS,
MomentumEquationWithStress,
HookesDeviatoricStressRate,
MonaghanArtificialStress)
equations = []
g1 = []
all = self.solids + self.elastic_solids
for elastic_solid in self.elastic_solids:
g1.append(
# p
IsothermalEOS(elastic_solid, sources=None))
g1.append(
# vi,j : requires properties v00, v01, v10, v11
VelocityGradient2D(dest=elastic_solid, sources=all))
g1.append(
# rij : requires properties r00, r01, r02, r11, r12, r22,
# s00, s01, s02, s11, s12, s22
MonaghanArtificialStress(dest=elastic_solid,
sources=None,
eps=self.artificial_stress_eps))
equations.append(Group(equations=g1))
g2 = []
for elastic_solid in self.elastic_solids:
g2.append(ContinuityEquation(dest=elastic_solid, sources=all), )
g2.append(
# au, av
MomentumEquationWithStress(dest=elastic_solid, sources=all), )
g2.append(
# au, av
MonaghanArtificialViscosity(dest=elastic_solid,
sources=all,
alpha=self.alpha,
beta=self.beta), )
g2.append(
# a_s00, a_s01, a_s11
HookesDeviatoricStressRate(dest=elastic_solid, sources=None), )
g2.append(
# ax, ay, az
XSPHCorrection(dest=elastic_solid,
sources=[elastic_solid],
eps=self.xsph_eps), )
equations.append(Group(g2))
return equations
def create_equations(self):
equations = [
Group(equations=[
BodyForce(dest='cube', sources=None, gy=-9.81),
SummationDensity(dest='cube', sources=['fluid', 'cube'])
],
real=False),
Group(equations=[
TaitEOSHGCorrection(dest='cube',
sources=None,
rho0=self.solid_rho,
c0=self.co,
gamma=7.0),
TaitEOSHGCorrection(dest='fluid',
sources=None,
rho0=self.ro,
c0=self.co,
gamma=7.0),
TaitEOSHGCorrection(dest='tank',
sources=None,
rho0=self.ro,
c0=self.co,
gamma=7.0),
],
real=False),
Group(equations=[
ContinuityEquation(
dest='fluid',
sources=['fluid', 'tank', 'cube'],
),
ContinuityEquation(
dest='tank',
sources=['fluid', 'tank', 'cube'],
),
MomentumEquation(dest='fluid',
sources=['fluid', 'tank', 'cube'],
alpha=self.alpha,
beta=0.0,
c0=self.co,
gy=-9.81),
LiuFluidForce(
dest='fluid',
sources=['cube'],
),
XSPHCorrection(dest='fluid', sources=['fluid', 'tank']),
]),
Group(equations=[
RigidBodyCollision(dest='cube', sources=['tank'], kn=1e5)
]),
Group(equations=[RigidBodyMoments(dest='cube', sources=None)]),
Group(equations=[RigidBodyMotion(dest='cube', sources=None)]),
]
return equations
def create_equations(self):
# Formulation for REF1
# (using only first set of equations for simplicity)
equations = [
# For the multi-phase formulation, we require an estimate of the
# particle volume. This can be either defined from the particle
# number density or simply as the ratio of mass to density
Group(equations=[
VolumeFromMassDensity(dest='fluid', sources=None)
], ),
# Equation of state is typically the Tait EOS with a suitable
# exponent gamma
Group(equations=[
TaitEOSHGCorrectionVariableRho(dest='fluid', sources=None, c0=c0, gamma=gamma),
], ),
# The boundary conditions are imposed by extrapolating the fluid
# pressure, taking into consideration the boundary acceleration
Group(equations=[
SolidWallPressureBC(dest='solid', sources=['fluid'], b=1.0, gy=gravity_y,
rho0=rho0, p0=p0)
], ),
# Main acceleration block
Group(equations=[
# Continuity equation
ContinuityEquation(dest='fluid', sources=['fluid', 'solid']),
# Pressure gradient with acceleration damping
MomentumEquationPressureGradient(
dest='fluid', sources=['fluid', 'solid'], pb=0.0, gy=gravity_y,
tdamp=tdamp),
# artificial viscosity for stability
MomentumEquationArtificialViscosity(
dest='fluid', sources=['fluid', 'solid'], alpha=0.24, c0=c0),
# Position step with XSPH
XSPHCorrection(dest='fluid', sources=['fluid'], eps=0.0)
]),
]
return equations
def create_equations(self):
equations = [
Group(equations=[
BodyForce(dest='cube', sources=None, gy=-9.81),
],
real=False),
Group(equations=[
ContinuityEquation(dest='fluid',
sources=['fluid', 'tank', 'cube']),
ContinuityEquation(dest='tank',
sources=['tank', 'fluid', 'cube'])
]),
# Tait equation of state
Group(equations=[
TaitEOSHGCorrection(dest='fluid',
sources=None,
rho0=self.ro,
c0=self.co,
gamma=7.0),
TaitEOSHGCorrection(dest='tank',
sources=None,
rho0=self.ro,
c0=self.co,
gamma=7.0),
],
real=False),
Group(equations=[
MomentumEquation(dest='fluid',
sources=['fluid', 'tank'],
alpha=self.alpha,
beta=0.0,
c0=self.co,
gy=-9.81),
AkinciRigidFluidCoupling(dest='fluid', sources=['cube']),
XSPHCorrection(dest='fluid', sources=['fluid', 'tank']),
]),
Group(equations=[
RigidBodyCollision(
dest='cube', sources=['tank', 'cube'], kn=1e5)
]),
Group(equations=[RigidBodyMoments(dest='cube', sources=None)]),
Group(equations=[RigidBodyMotion(dest='cube', sources=None)]),
]
return equations
def create_equations(self):
print("Create our own equations.")
equations = [
Group(equations=[
TaitEOS(dest='fluid',
sources=None,
rho0=self.ro,
c0=self.co,
gamma=7.0),
],
real=False),
Group(equations=[
ContinuityEquation(dest='fluid', sources=['fluid']),
MomentumEquation(dest='fluid',
sources=['fluid'],
alpha=self.alpha,
beta=0.0,
c0=self.co),
XSPHCorrection(dest='fluid', sources=['fluid']),
]),
]
return equations
def create_equations(self):
equations = [
# Equation of state
Group(equations=[
TaitEOS(dest='fluid',
sources=None,
rho0=rho0,
c0=c0,
gamma=gamma),
TaitEOSHGCorrection(dest='boundary',
sources=None,
rho0=rho0,
c0=c0,
gamma=gamma),
],
real=False),
# Continuity Momentum and XSPH equations
Group(equations=[
ContinuityEquation(dest='fluid', sources=['fluid', 'boundary'
]),
ContinuityEquation(dest='boundary', sources=['fluid']),
MomentumEquation(dest='fluid',
sources=['fluid', 'boundary'],
c0=c0,
alpha=alpha,
beta=beta,
gz=-9.81,
tensile_correction=True),
# Position step with XSPH
XSPHCorrection(dest='fluid', sources=['fluid'], eps=eps)
])
]
return equations
def _get_external_flow_equations(self):
from pysph.sph.basic_equations import XSPHCorrection
from pysph.sph.wc.transport_velocity import (
VolumeSummation, SolidWallNoSlipBC, SummationDensity,
MomentumEquationArtificialViscosity,
MomentumEquationViscosity
)
iom = self.inlet_outlet_manager
fluids_with_io = self.fluids
all_solids = self.solids + self.inviscid_solids
if iom is not None:
fluids_with_io = self.fluids + iom.get_io_names()
all = fluids_with_io + all_solids
edac_nu = self._get_edac_nu()
equations = []
# inlet-outlet
if iom is not None:
io_eqns = iom.get_equations(self, self.use_tvf)
for grp in io_eqns:
equations.append(grp)
group1 = []
for fluid in fluids_with_io:
group1.append(SummationDensity(dest=fluid, sources=all))
for solid in self.solids:
group1.extend([
SourceNumberDensity(dest=solid, sources=fluids_with_io),
VolumeSummation(dest=solid, sources=all),
SolidWallPressureBC(dest=solid, sources=fluids_with_io,
gx=self.gx, gy=self.gy, gz=self.gz),
SetWallVelocity(dest=solid, sources=fluids_with_io),
])
if self.clamp_p:
group1.append(
ClampWallPressure(dest=solid, sources=None)
)
for solid in self.inviscid_solids:
group1.extend([
SourceNumberDensity(dest=solid, sources=fluids_with_io),
NoSlipVelocityExtrapolation(
dest=solid, sources=fluids_with_io),
VolumeSummation(dest=solid, sources=all),
SolidWallPressureBC(dest=solid, sources=fluids_with_io,
gx=self.gx, gy=self.gy, gz=self.gz)
])
equations.append(Group(equations=group1, real=False))
group2 = []
for fluid in self.fluids:
group2.append(
MomentumEquation(
dest=fluid, sources=all, gx=self.gx, gy=self.gy,
gz=self.gz, c0=self.c0, tdamp=self.tdamp
)
)
if self.alpha > 0.0:
sources = fluids_with_io + self.solids
group2.append(
MomentumEquationArtificialViscosity(
dest=fluid, sources=sources, alpha=self.alpha,
c0=self.c0
)
)
if self.nu > 0.0:
group2.append(
MomentumEquationViscosity(
dest=fluid, sources=fluids_with_io, nu=self.nu
)
)
if len(self.solids) > 0 and self.nu > 0.0:
group2.append(
SolidWallNoSlipBC(
dest=fluid, sources=self.solids, nu=self.nu
)
)
group2.extend([
EDACEquation(
dest=fluid, sources=all, nu=edac_nu, cs=self.c0,
rho0=self.rho0
),
XSPHCorrection(dest=fluid, sources=[fluid],
eps=self.eps)
])
equations.append(Group(equations=group2))
# inlet-outlet
if iom is not None:
io_eqns = iom.get_equations_post_compute_acceleration()
for grp in io_eqns:
equations.append(grp)
return equations
def create_equations(self):
equations = [
# We first compute the mass and number density of the fluid
# phase. This is used in all force computations henceforth. The
# number density (1/volume) is explicitly set for the solid phase
# and this isn't modified for the simulation.
Group(equations=[
SummationDensity(dest='fluid', sources=['fluid', 'wall'])
]),
# Given the updated number density for the fluid, we can update
# the fluid pressure. Additionally, we compute the gradient of the
# color function with respect to the original smoothing
# length. This will compute the interface normals. Also compute
# the smoothed color based on the color index for a particle.
Group(equations=[
IsothermalEOS(
dest='fluid', sources=None, rho0=rho0, c0=c0, p0=p0),
SmoothedColor(dest='fluid', sources=['fluid']),
]),
#################################################################
# Begin Surface tension formulation
#################################################################
# Scale the smoothing lengths to determine the interface
# quantities. The NNPS need not be updated since the smoothing
# length is decreased.
Group(equations=[
ScaleSmoothingLength(dest='fluid', sources=None, factor=0.8)
],
update_nnps=False),
# Compute the gradient of the color function with respect to the
# new smoothing length. At the end of this Group, we will have the
# interface normals and the discretized dirac delta function for
# the fluid-fluid interface.
Group(equations=[
ColorGradientUsingNumberDensity(dest='fluid',
sources=['fluid', 'wall']),
], ),
# Compute the interface curvature using the modified smoothing
# length and interface normals computed in the previous Group.
Group(equations=[
InterfaceCurvatureFromNumberDensity(dest='fluid',
sources=['fluid']),
], ),
# Now rescale the smoothing length to the original value for the
# rest of the computations.
Group(
equations=[
ScaleSmoothingLength(dest='fluid',
sources=None,
factor=1.25)
],
update_nnps=False,
),
#################################################################
# End Surface tension formulation
#################################################################
# Once the pressure for the fluid phase has been updated via the
# state-equation, we can extrapolate the pressure to the wall
# ghost particles. After this group, the density and pressure of
# the boundary particles has been updated and can be used in the
# integration equations.
Group(equations=[
SolidWallPressureBC(dest='wall',
sources=['fluid'],
p0=p0,
rho0=rho0,
gy=gy,
b=1.0),
], ),
# The main acceleration block
Group(
equations=[
# Body force due to gravity
BodyForce(dest='fluid', sources=None, fy=gy),
# Gradient of pressure for the fluid phase using the
# number density formulation. The no-penetration boundary
# condition is taken care of by using the boundary
# pressure and density.
PressureGradientUsingNumberDensity(
dest='fluid', sources=['fluid', 'wall']),
# Artificial viscosity for the fluid phase.
ClearyArtificialViscosity(dest='fluid',
sources=['fluid', 'wall'],
dim=dim,
alpha=alpha),
# Surface tension force for the SY11 formulation
ShadlooYildizSurfaceTensionForce(dest='fluid',
sources=None,
sigma=sigma),
# XSPH Correction
XSPHCorrection(dest='fluid', sources=['fluid'], eps=0.1),
], )
]
return equations
def create_equations(self):
# Formulation for REF1
equations1 = [
# For the multi-phase formulation, we require an estimate of the
# particle volume. This can be either defined from the particle
# number density or simply as the ratio of mass to density.
Group(equations=[
VolumeFromMassDensity(dest='fluid', sources=None)
], ),
# Equation of state is typically the Tait EOS with a suitable
# exponent gamma
Group(equations=[
TaitEOS(
dest='fluid',
sources=None,
rho0=rho0,
c0=c0,
gamma=gamma),
], ),
# The boundary conditions are imposed by extrapolating the fluid
# pressure, taking into considering the bounday acceleration
Group(equations=[
SolidWallPressureBC(dest='solid', sources=['fluid'], b=1.0, gy=gy,
rho0=rho0, p0=p0),
], ),
# Main acceleration block
Group(equations=[
# Continuity equation
ContinuityEquation(
dest='fluid', sources=[
'fluid', 'solid']),
# Pressure gradient with acceleration damping.
MomentumEquationPressureGradient(
dest='fluid', sources=['fluid', 'solid'], pb=0.0, gy=gy,
tdamp=tdamp),
# artificial viscosity for stability
MomentumEquationArtificialViscosity(
dest='fluid', sources=['fluid', 'solid'], alpha=0.24, c0=c0),
# Position step with XSPH
XSPHCorrection(dest='fluid', sources=['fluid'], eps=0.0)
]),
]
# Formulation for REF2. Note that for this formulation to work, the
# boundary particles need to have a spacing different from the fluid
# particles (usually determined by a factor beta). In the current
# implementation, the value is taken as 1.0 which will mostly be
# ineffective.
equations2 = [
# For the multi-phase formulation, we require an estimate of the
# particle volume. This can be either defined from the particle
# number density or simply as the ratio of mass to density.
Group(equations=[
VolumeFromMassDensity(dest='fluid', sources=None)
], ),
# Equation of state is typically the Tait EOS with a suitable
# exponent gamma
Group(equations=[
TaitEOS(
dest='fluid',
sources=None,
rho0=rho0,
c0=c0,
gamma=gamma),
], ),
# Main acceleration block
Group(equations=[
# The boundary conditions are imposed as a force or
# accelerations on the fluid particles. Note that the
# no-penetration condition is to be satisfied with this
# equation. The subsequent equations therefore do not have
# solid as the source. Note the difference between the
# ghost-fluid formulations. K should be 0.01*co**2
# according to REF2. We take it much smaller here on
# account of the multiple layers of boundary particles
MonaghanKajtarBoundaryForce(dest='fluid', sources=['solid'],
K=0.02, beta=1.0, h=hdx * dx),
# Continuity equation
ContinuityEquation(dest='fluid', sources=['fluid', ]),
# Pressure gradient with acceleration damping.
MomentumEquationPressureGradient(
dest='fluid', sources=['fluid'], pb=0.0, gy=gy,
tdamp=tdamp),
# artificial viscosity for stability
MomentumEquationArtificialViscosity(
dest='fluid', sources=['fluid'], alpha=0.25, c0=c0),
# Position step with XSPH
XSPHCorrection(dest='fluid', sources=['fluid'], eps=0.0)
]),
]
# Formulation for REF3
equations3 = [
# For the multi-phase formulation, we require an estimate of the
# particle volume. This can be either defined from the particle
# number density or simply as the ratio of mass to density.
Group(equations=[
VolumeFromMassDensity(dest='fluid', sources=None)
], ),
# Equation of state is typically the Tait EOS with a suitable
# exponent gamma. The solid phase is treated just as a fluid and
# the pressure and density operations is updated for this as well.
Group(equations=[
TaitEOS(
dest='fluid',
sources=None,
rho0=rho0,
c0=c0,
gamma=gamma),
TaitEOS(
dest='solid',
sources=None,
rho0=rho0,
c0=c0,
gamma=gamma),
], ),
# Main acceleration block. The boundary conditions are imposed by
# peforming the continuity equation and gradient of pressure
# calculation on the solid phase, taking contributions from the
# fluid phase
Group(equations=[
# Continuity equation
ContinuityEquation(
dest='fluid', sources=[
'fluid', 'solid']),
ContinuityEquation(dest='solid', sources=['fluid']),
# Pressure gradient with acceleration damping.
MomentumEquationPressureGradient(
dest='fluid', sources=['fluid', 'solid'], pb=0.0, gy=gy,
tdamp=tdamp),
# artificial viscosity for stability
MomentumEquationArtificialViscosity(
dest='fluid', sources=['fluid', 'solid'], alpha=0.25, c0=c0),
# Position step with XSPH
XSPHCorrection(dest='fluid', sources=['fluid'], eps=0.5)
]),
]
if self.options.bc_type == 1:
return equations1
elif self.options.bc_type == 2:
return equations2
elif self.options.bc_type == 3:
return equations3
def get_equations(self):
from pysph.sph.equation import Group
from pysph.sph.wc.basic import (MomentumEquation, TaitEOS,
TaitEOSHGCorrection,
UpdateSmoothingLengthFerrari)
from pysph.sph.wc.basic import (ContinuityEquationDeltaSPH,
MomentumEquationDeltaSPH)
from pysph.sph.basic_equations import \
(ContinuityEquation, SummationDensity, XSPHCorrection)
from pysph.sph.wc.viscosity import LaminarViscosity
equations = []
g1 = []
all = self.fluids + self.solids
if self.summation_density:
g0 = []
for name in self.fluids:
g0.append(SummationDensity(dest=name, sources=all))
equations.append(Group(equations=g0, real=False))
for name in self.fluids:
g1.append(
TaitEOS(dest=name,
sources=None,
rho0=self.rho0,
c0=self.c0,
gamma=self.gamma))
if self.hg_correction:
# This correction applies only to solids.
for name in self.solids:
g1.append(
TaitEOSHGCorrection(dest=name,
sources=None,
rho0=self.rho0,
c0=self.c0,
gamma=self.gamma))
equations.append(Group(equations=g1, real=False))
g2 = []
for name in self.solids:
g2.append(ContinuityEquation(dest=name, sources=self.fluids))
for name in self.fluids:
if self.delta_sph:
other = all[:]
other.remove(name)
g2.append(
ContinuityEquationDeltaSPH(dest=name,
sources=[name],
c0=self.c0,
delta=self.delta))
if len(other) > 0:
g2.append(ContinuityEquation(dest=name, sources=other))
g2.append(
MomentumEquationDeltaSPH(
dest=name,
sources=[name],
rho0=self.rho0,
c0=self.c0,
alpha=self.alpha,
gx=self.gx,
gy=self.gy,
gz=self.gz,
))
if len(other) > 0:
g2.append(
MomentumEquation(
dest=name,
sources=other,
c0=self.c0,
alpha=self.alpha,
beta=self.beta,
gx=self.gx,
gy=self.gy,
gz=self.gz,
tensile_correction=self.tensile_correction))
g2.append(XSPHCorrection(dest=name, sources=[name]))
else:
if not self.summation_density:
g2.append(ContinuityEquation(dest=name, sources=all))
g2.extend([
MomentumEquation(
dest=name,
sources=all,
alpha=self.alpha,
beta=self.beta,
gx=self.gx,
gy=self.gy,
gz=self.gz,
c0=self.c0,
tensile_correction=self.tensile_correction),
XSPHCorrection(dest=name, sources=[name])
])
if abs(self.nu) > 1e-14:
eq = LaminarViscosity(dest=name,
sources=self.fluids,
nu=self.nu)
g2.insert(-1, eq)
equations.append(Group(equations=g2))
if self.update_h:
g3 = [
UpdateSmoothingLengthFerrari(dest=x,
sources=None,
dim=self.dim,
hdx=self.hdx) for x in self.fluids
]
equations.append(Group(equations=g3, real=False))
return equations
def create_equations(self):
equations = [
# Properties computed set from the current state
Group(
equations=[
# p
IsothermalEOS(dest='solid',
sources=None,
rho0=rho0,
c0=c0,
p0=0.0),
# vi,j : requires properties v00, v01, v10, v11
VelocityGradient2D(dest='solid', sources=[
'solid',
]),
# rij : requires properties r00, r01, r02, r11, r12, r22,
# s00, s01, s02, s11, s12, s22
MonaghanArtificialStress(dest='solid',
sources=None,
eps=0.3),
], ),
# Acceleration variables are now computed
Group(equations=[
# arho
ContinuityEquation(dest='solid', sources=[
'solid',
]),
# au, av
MomentumEquationWithStress(dest='solid',
sources=[
'solid',
],
n=4,
wdeltap=self.wdeltap),
# au, av
MonaghanArtificialViscosity(dest='solid',
sources=[
'solid',
],
alpha=1.0,
beta=1.0),
# a_s00, a_s01, a_s11
HookesDeviatoricStressRate(dest='solid',
sources=None,
shear_mod=G),
# ax, ay, az
XSPHCorrection(dest='solid', sources=[
'solid',
], eps=0.5),
]) # End Acceleration Group
] # End Group list
return equations
def _get_external_flow_equations(self):
from pysph.sph.basic_equations import XSPHCorrection
from pysph.sph.wc.transport_velocity import (
VolumeSummation, SolidWallNoSlipBC, SummationDensity,
MomentumEquationArtificialViscosity, MomentumEquationViscosity)
all_solids = self.solids + self.inviscid_solids
all = self.fluids + all_solids
edac_nu = self._get_edac_nu()
equations = []
group1 = []
for fluid in self.fluids:
group1.append(SummationDensity(dest=fluid, sources=all))
for solid in self.solids:
group1.extend([
SourceNumberDensity(dest=solid, sources=self.fluids),
VolumeSummation(dest=solid, sources=all),
SolidWallPressureBC(dest=solid,
sources=self.fluids,
gx=self.gx,
gy=self.gy,
gz=self.gz),
SetWallVelocity(dest=solid, sources=self.fluids),
])
if self.clamp_p:
group1.append(ClampWallPressure(dest=solid, sources=None))
for solid in self.inviscid_solids:
group1.extend([
SourceNumberDensity(dest=solid, sources=self.fluids),
NoSlipVelocityExtrapolation(dest=solid, sources=self.fluids),
VolumeSummation(dest=solid, sources=all),
SolidWallPressureBC(dest=solid,
sources=self.fluids,
gx=self.gx,
gy=self.gy,
gz=self.gz)
])
equations.append(Group(equations=group1, real=False))
group2 = []
for fluid in self.fluids:
group2.append(
MomentumEquation(dest=fluid,
sources=all,
gx=self.gx,
gy=self.gy,
gz=self.gz,
c0=self.c0,
tdamp=self.tdamp))
if self.alpha > 0.0:
group2.append(
MomentumEquationArtificialViscosity(dest=fluid,
sources=all,
alpha=self.alpha,
c0=self.c0))
if self.nu > 0.0:
group2.append(
MomentumEquationViscosity(dest=fluid,
sources=self.fluids,
nu=self.nu))
if len(self.solids) > 0 and self.nu > 0.0:
group2.append(
SolidWallNoSlipBC(dest=fluid,
sources=self.solids,
nu=self.nu))
group2.extend([
EDACEquation(dest=fluid,
sources=all,
nu=edac_nu,
cs=self.c0,
rho0=self.rho0),
XSPHCorrection(dest=fluid, sources=[fluid], eps=self.eps)
])
equations.append(Group(equations=group2))
return equations
ContinuityEquationDeltaSPH(
dest='fluid', sources=['fluid'], c0=co, delta=0.1),
ContinuityEquation(dest='fluid', sources=['boundary']),
ContinuityEquation(dest='boundary', sources=['fluid']),
# Momentum equation
MomentumEquation(dest='fluid',
sources=['fluid', 'boundary'],
alpha=alpha,
beta=beta,
gy=-9.81,
c0=co,
tensile_correction=True),
# Position step with XSPH
XSPHCorrection(dest='fluid', sources=['fluid'])
]),
# smoothing length update
Group(equations=[
UpdateSmoothingLengthFerrari(dest='fluid',
sources=None,
hdx=1.2,
dim=2)
],
real=True),
]
# Setup the application and solver. This also generates the particles.
app.setup(solver=solver,
equations=equations,
def create_equations(self):
equations = [
# Properties computed set from the current state
Group(
equations=[
# p
MieGruneisenEOS(dest='bar',
sources=None,
gamma=gamma,
r0=r0,
c0=C,
S=S),
# vi,j : requires properties v00, v01, v10, v11
VelocityGradient2D(dest='bar', sources=[
'bar',
]),
# rij : requires properties s00, s01, s11
VonMisesPlasticity2D(flow_stress=Yo,
dest='bar',
sources=None),
], ),
# Acceleration variables are now computed
Group(equations=[
# arho
ContinuityEquation(dest='bar', sources=['bar']),
# au, av
MomentumEquationWithStress(dest='bar', sources=['bar']),
# au, av
MonaghanArtificialViscosity(dest='bar',
sources=['bar'],
alpha=0.5,
beta=0.5),
# au av
MonaghanBoundaryForce(dest='bar', sources=['plate'],
deltap=dx),
# ae
EnergyEquationWithStress(dest='bar',
sources=['bar'],
alpha=0.5,
beta=0.5,
eta=0.01),
# a_s00, a_s01, a_s11
HookesDeviatoricStressRate(dest='bar', sources=None),
# ax, ay, az
XSPHCorrection(dest='bar', sources=[
'bar',
], eps=0.5),
]) # End Acceleration Group
] # End Group list
return equations
def create_equations(self):
equations = [
Group(
equations=[
BodyForce(dest='cube', sources=None, gy=-9.81),
BodyForce(dest='wood', sources=None, gy=-9.81),
BodyForce(dest='small_tank', sources=None, gy=-9.81),
BodyForce(dest='outside', sources=None, gy=-9.81),
SummationDensity(dest='cube', sources=['fluid', 'cube']),
SummationDensity(dest='wood', sources=['fluid', 'wood']),
SummationDensity(dest='small_tank',
sources=['fluid', 'small_tank']),
SummationDensity(dest='outside',
sources=['fluid', 'outside'])
# NumberDensity(dest='cube', sources=['cube']),
],
real=False),
Group(equations=[
TaitEOSHGCorrection(dest='wood',
sources=None,
rho0=self.wood_rho,
c0=self.co,
gamma=7.0),
TaitEOSHGCorrection(dest='cube',
sources=None,
rho0=self.solid_rho,
c0=self.co,
gamma=7.0),
TaitEOSHGCorrection(dest='fluid',
sources=None,
rho0=self.ro,
c0=self.co,
gamma=7.0),
TaitEOSHGCorrection(dest='big_tank',
sources=None,
rho0=self.ro,
c0=self.co,
gamma=7.0),
TaitEOSHGCorrection(dest='small_tank',
sources=None,
rho0=self.wood_rho,
c0=self.co,
gamma=7.0),
TaitEOSHGCorrection(dest='outside',
sources=None,
rho0=self.ro,
c0=self.co,
gamma=7.0),
],
real=False),
Group(equations=[
ContinuityEquation(
dest='fluid',
sources=[
'fluid', 'small_tank', 'cube', 'wood', 'big_tank',
'outside'
],
),
ContinuityEquation(
dest='big_tank',
sources=[
'fluid', 'big_tank', 'cube', 'wood', 'small_tank',
'outside'
],
),
MomentumEquation(dest='fluid',
sources=['fluid', 'big_tank'],
alpha=self.alpha,
beta=0.0,
c0=self.co,
gy=-9.81),
LiuFluidForce(
dest='fluid',
sources=['cube'],
),
LiuFluidForce(
dest='fluid',
sources=['wood'],
),
LiuFluidForce(
dest='fluid',
sources=['small_tank'],
),
LiuFluidForce(
dest='fluid',
sources=['outside'],
),
# PressureRigidBody(dest='fluid', sources=['cube'],
# rho0=1500),
XSPHCorrection(dest='fluid', sources=['fluid', 'big_tank']),
]),
Group(equations=[
RigidBodyCollision(
dest='cube',
sources=['big_tank', 'wood', 'small_tank', 'outside'],
kn=1e6)
]),
Group(equations=[RigidBodyMoments(dest='cube', sources=None)]),
Group(equations=[RigidBodyMotion(dest='cube', sources=None)]),
Group(equations=[
RigidBodyCollision(
dest='wood',
sources=['big_tank', 'cube', 'small_tank', 'outside'],
kn=1e6)
]),
Group(equations=[RigidBodyMoments(dest='wood', sources=None)]),
Group(equations=[RigidBodyMotion(dest='wood', sources=None)]),
Group(equations=[
RigidBodyCollision(
dest='small_tank',
sources=['big_tank', 'cube', 'wood', 'outside'],
kn=1e6)
]),
Group(
equations=[RigidBodyMoments(dest='small_tank', sources=None)]),
Group(
equations=[RigidBodyMotion(dest='small_tank', sources=None)]),
Group(equations=[
RigidBodyCollision(
dest='outside',
sources=['big_tank', 'cube', 'small_tank', 'wood'],
kn=1e6)
]),
Group(equations=[RigidBodyMoments(dest='outside', sources=None)]),
Group(equations=[RigidBodyMotion(dest='outside', sources=None)]),
]
return equations
def create_equations(self):
equations = [
Group(equations=[
BodyForce(dest='block', sources=None, gy=gy),
NumberDensity(dest='block', sources=['block']),
NumberDensity(dest='solid', sources=['solid']),
], ),
# Equation of state is typically the Tait EOS with a suitable
# exponent gamma
Group(equations=[
TaitEOS(dest='fluid',
sources=None,
rho0=rho0,
c0=c0,
gamma=gamma),
TaitEOSHGCorrection(dest='solid',
sources=None,
rho0=rho0,
c0=c0,
gamma=gamma),
TaitEOSHGCorrection(dest='block',
sources=None,
rho0=rho0,
c0=c0,
gamma=gamma),
], ),
# Main acceleration block
Group(equations=[
# Continuity equation with dissipative corrections for fluid on fluid
ContinuityEquationDeltaSPH(
dest='fluid', sources=['fluid'], c0=c0, delta=0.1),
ContinuityEquation(dest='fluid', sources=['solid', 'block']),
ContinuityEquation(dest='solid', sources=['fluid']),
ContinuityEquation(dest='block', sources=['fluid']),
# Momentum equation
MomentumEquation(dest='fluid',
sources=['fluid', 'solid', 'block'],
alpha=alpha,
beta=beta,
gy=-9.81,
c0=c0,
tensile_correction=True),
PressureRigidBody(dest='fluid',
sources=['block', 'solid'],
rho0=rho0),
ViscosityRigidBody(
dest='fluid', sources=['block', 'solid'
], rho0=rho0, nu=nu),
# Position step with XSPH
XSPHCorrection(dest='fluid', sources=['fluid']),
RigidBodyCollision(dest='block',
sources=['solid'],
k=1.0,
d=2.0,
eta=0.1,
kt=0.1),
]),
Group(equations=[RigidBodyMoments(dest='block', sources=None)]),
Group(equations=[RigidBodyMotion(dest='block', sources=None)]),
]
return equations
def get_equations(self):
from pysph.sph.equation import Group
from pysph.sph.wc.basic import TaitEOS
from pysph.sph.basic_equations import XSPHCorrection
from pysph.sph.wc.transport_velocity import (
ContinuityEquation, MomentumEquationPressureGradient,
MomentumEquationViscosity, MomentumEquationArtificialViscosity,
SolidWallPressureBC, SolidWallNoSlipBC, SetWallVelocity,
VolumeSummation)
equations = []
all = self.fluids + self.solids
g2 = []
for fluid in self.fluids:
g2.append(VolumeSummation(dest=fluid, sources=all))
g2.append(
TaitEOS(dest=fluid,
sources=None,
rho0=self.rho0,
c0=self.c0,
gamma=self.gamma,
p0=self.p0))
for solid in self.solids:
g2.append(VolumeSummation(dest=solid, sources=all))
g2.append(SetWallVelocity(dest=solid, sources=self.fluids))
equations.append(Group(equations=g2, real=False))
g3 = []
for solid in self.solids:
g3.append(
SolidWallPressureBC(dest=solid,
sources=self.fluids,
b=1.0,
rho0=self.rho0,
p0=self.B,
gx=self.gx,
gy=self.gy,
gz=self.gz))
equations.append(Group(equations=g3, real=False))
g4 = []
for fluid in self.fluids:
g4.append(ContinuityEquation(dest=fluid, sources=all))
g4.append(
MomentumEquationPressureGradient(dest=fluid,
sources=all,
pb=0.0,
gx=self.gx,
gy=self.gy,
gz=self.gz,
tdamp=self.tdamp))
if self.alpha > 0.0:
g4.append(
MomentumEquationArtificialViscosity(dest=fluid,
sources=all,
c0=self.c0,
alpha=self.alpha))
if self.nu > 0.0:
g4.append(
MomentumEquationViscosity(dest=fluid,
sources=self.fluids,
nu=self.nu))
if len(self.solids) > 0:
g4.append(
SolidWallNoSlipBC(dest=fluid,
sources=self.solids,
nu=self.nu))
g4.append(XSPHCorrection(dest=fluid, sources=[fluid]))
equations.append(Group(equations=g4))
return equations
def create_equations(self):
# Formulation for REF1
equations1 = [
# Spoon Equations
Group(
equations=[
HarmonicOscilllator(dest='spoon',
sources=None,
A=0.5,
omega=0.2),
# Translate acceleration to positions
XSPHCorrection(dest='spoon', sources=['spoon'], eps=0.0)
],
real=False),
# Water Faucet Equations
Group(equations=[
H2OFaucet(dest='tahini',
sources=None,
x=1.25,
y=tahiniH,
r=0.15,
fill_rate=7),
DiffuseH2O(
dest='tahini', sources=['tahini'], diffusion_speed=0.1),
]),
# For the multi-phase formulation, we require an estimate of the
# particle volume. This can be either defined from the particle
# number density or simply as the ratio of mass to density.
Group(
equations=[VolumeFromMassDensity(dest='tahini',
sources=None)], ),
# Equation of state is typically the Tait EOS with a suitable
# exponent gamma
Group(equations=[
TaitEOSHGCorrection(dest='tahini',
sources=None,
rho0=rho0,
c0=c0,
gamma=gamma),
], ),
# The boundary conditions are imposed by extrapolating the tahini
# pressure, taking into considering the bounday acceleration
Group(equations=[
SolidWallPressureBC(dest='bowl',
sources=['tahini'],
b=1.0,
gy=gy,
rho0=rho0,
p0=p0),
SolidWallPressureBC(dest='spoon',
sources=['tahini'],
b=1.0,
gy=gy,
rho0=rho0,
p0=p0),
], ),
# Main acceleration block
Group(equations=[
TahiniEquation(
dest='tahini', sources=['tahini'], sigma=dx / 1.122),
# Continuity equation
ContinuityEquation(dest='tahini',
sources=['tahini', 'bowl', 'spoon']),
# Pressure gradient with acceleration damping.
MomentumEquationPressureGradient(
dest='tahini',
sources=['tahini', 'bowl', 'spoon'],
pb=0.0,
gy=gy,
tdamp=tdamp),
# artificial viscosity for stability
MomentumEquationArtificialViscosity(
dest='tahini',
sources=['tahini', 'bowl', 'spoon'],
alpha=1,
c0=c0),
# Position step with XSPH
XSPHCorrection(dest='tahini', sources=['tahini'], eps=0.0)
]),
]
# Formulation for REF3
equations3 = [
# Spoon Equations
Group(
equations=[
HarmonicOscilllator(dest='spoon',
sources=None,
A=0.5,
omega=0.2),
# Translate acceleration to positions
XSPHCorrection(dest='spoon', sources=['spoon'], eps=0.0)
],
real=False),
# Water Faucet Equations
Group(equations=[
H2OFaucet(dest='tahini',
sources=None,
x=Cx,
y=tahiniH,
r=0.15,
fill_rate=5),
DiffuseH2O(
dest='tahini', sources=['tahini'], diffusion_speed=0.1),
]),
# For the multi-phase formulation, we require an estimate of the
# particle volume. This can be either defined from the particle
# number density or simply as the ratio of mass to density.
Group(
equations=[VolumeFromMassDensity(dest='tahini',
sources=None)], ),
# Equation of state is typically the Tait EOS with a suitable
# exponent gamma. The solid phase is treated just as a fluid and
# the pressure and density operations is updated for this as well.
Group(equations=[
TaitEOS(dest='tahini',
sources=None,
rho0=rho0,
c0=c0,
gamma=gamma),
TaitEOS(dest='bowl',
sources=None,
rho0=rho0,
c0=c0,
gamma=gamma),
TaitEOS(dest='spoon',
sources=None,
rho0=rho0,
c0=c0,
gamma=gamma),
], ),
# Main acceleration block. The boundary conditions are imposed by
# peforming the continuity equation and gradient of pressure
# calculation on the bowl phase, taking contributions from the
# tahini phase
Group(equations=[
TahiniEquation(
dest='tahini', sources=['tahini'], sigma=dx / 1.122),
# Continuity equation
ContinuityEquation(dest='tahini',
sources=['tahini', 'bowl', 'spoon']),
ContinuityEquation(dest='bowl', sources=['tahini']),
ContinuityEquation(dest='spoon', sources=['tahini']),
# Pressure gradient with acceleration damping.
MomentumEquationPressureGradient(
dest='tahini',
sources=['tahini', 'bowl', 'spoon'],
pb=0.0,
gy=gy,
tdamp=tdamp),
# artificial viscosity for stability
MomentumEquationArtificialViscosity(
dest='tahini',
sources=['tahini', 'bowl', 'spoon'],
alpha=1,
c0=c0),
# Position step with XSPH
XSPHCorrection(dest='tahini', sources=['tahini'], eps=0.5)
]),
]
if self.options.bc_type == 1:
return equations1
elif self.options.bc_type == 3:
return equations3
def create_equations(self):
h0 = dx * hdx
co = 10.0 * self.geom.get_max_speed(g=9.81)
gamma = 7.0
alpha = 0.5
beta = 0.0
B = co * co * rho0 / gamma
equations = [
Group(equations=[
BodyForce(dest='obstacle', sources=None, gz=-9.81),
NumberDensity(dest='obstacle', sources=['obstacle']),
NumberDensity(dest='boundary', sources=['boundary']),
], ),
# Equation of state
Group(equations=[
TaitEOS(dest='fluid',
sources=None,
rho0=rho0,
c0=co,
gamma=gamma),
TaitEOSHGCorrection(dest='boundary',
sources=None,
rho0=rho0,
c0=co,
gamma=gamma),
TaitEOSHGCorrection(dest='obstacle',
sources=None,
rho0=rho0,
c0=co,
gamma=gamma),
],
real=False),
# Continuity, momentum and xsph equations
Group(equations=[
ContinuityEquation(dest='fluid',
sources=['fluid', 'boundary', 'obstacle']),
ContinuityEquation(dest='boundary', sources=['fluid']),
ContinuityEquation(dest='obstacle', sources=['fluid']),
MomentumEquation(dest='fluid',
sources=['fluid', 'boundary'],
alpha=alpha,
beta=beta,
gz=-9.81,
c0=co,
tensile_correction=True),
PressureRigidBody(dest='fluid',
sources=['obstacle'],
rho0=rho0),
XSPHCorrection(dest='fluid', sources=['fluid']),
RigidBodyCollision(dest='obstacle',
sources=['boundary'],
k=1.0,
d=2.0,
eta=0.1,
kt=0.1),
]),
Group(equations=[RigidBodyMoments(dest='obstacle', sources=None)]),
Group(equations=[RigidBodyMotion(dest='obstacle', sources=None)]),
]
return equations
def create_equations(self):
equations = [
# update smoothing length
# Group(
# equations = [
# UpdateSmoothingLengthFromVolume(dest='plate', sources=['plate', 'projectile'], dim=dim, k=hdx),
# UpdateSmoothingLengthFromVolume(dest='projectile', sources=['plate', 'projectile'], dim=dim, k=hdx),
# ],
# update_nnps=True,
# ),
# compute properties from the current state
Group(equations=[
# EOS (compute the pressure using one of the EOSs)
# MieGruneisenEOS(dest='plate', sources=None, gamma=gamma1, r0=ro1 , c0=C1, S=S1),
# MieGruneisenEOS(dest='projectile', sources=None, gamma=gamma2, r0=ro2 , c0=C2, S=S2),
StiffenedGasEOS(
dest='plate', sources=None, gamma=gamma1, r0=ro1, c0=C1),
StiffenedGasEOS(dest='projectile',
sources=None,
gamma=gamma2,
r0=ro2,
c0=C2),
# compute the velocity gradient tensor
VelocityGradient3D(dest='plate', sources=['plate']),
VelocityGradient3D(dest='projectile', sources=['projectile']),
# # stress
VonMisesPlasticity2D(
dest='plate', sources=None, flow_stress=Yo1),
VonMisesPlasticity2D(
dest='projectile', sources=None, flow_stress=Yo2),
# # artificial stress to avoid clumping
MonaghanArtificialStress(dest='plate', sources=None, eps=0.3),
MonaghanArtificialStress(
dest='projectile', sources=None, eps=0.3),
]),
# accelerations (rho, u, v, ...)
Group(equations=[
# continuity equation
ContinuityEquation(dest='plate',
sources=['projectile', 'plate']),
ContinuityEquation(dest='projectile',
sources=['projectile', 'plate']),
# momentum equation
MomentumEquationWithStress(dest='projectile',
sources=[
'projectile',
'plate',
]),
MomentumEquationWithStress(dest='plate',
sources=[
'projectile',
'plate',
]),
# energy equation:
EnergyEquationWithStress(dest='plate',
sources=[
'projectile',
'plate',
],
alpha=avisc_alpha,
beta=avisc_beta,
eta=avisc_eta),
EnergyEquationWithStress(dest='projectile',
sources=[
'projectile',
'plate',
],
alpha=avisc_alpha,
beta=avisc_beta,
eta=avisc_eta),
# avisc
MonaghanArtificialViscosity(dest='plate',
sources=['projectile', 'plate'],
alpha=avisc_alpha,
beta=avisc_beta),
MonaghanArtificialViscosity(dest='projectile',
sources=['projectile', 'plate'],
alpha=avisc_alpha,
beta=avisc_beta),
# updates to the stress term
HookesDeviatoricStressRate(
dest='plate', sources=None, shear_mod=1.),
HookesDeviatoricStressRate(
dest='projectile', sources=None, shear_mod=1.),
# position stepping
XSPHCorrection(dest='plate', sources=['plate'], eps=xsph_eps),
XSPHCorrection(
dest='projectile', sources=['projectile'], eps=xsph_eps),
]),
] # End Group list
return equations