def create_equations(self):
'''
Set-up governing equations
'''
equations = [
Group(equations=[
IsothermalEOS(dest='fluid',
sources=['fluid'],
rho0=self.rho0,
c0=self.c0,
p0=0.0),
GradientCorrectionPreStep(dest='fluid',
sources=['fluid'],
dim=2),
],
real=False),
Group(
equations=[
GradientCorrection(dest='fluid',
sources=['fluid'],
dim=2,
tol=0.1),
ContinuityEquationDeltaSPHPreStep(dest='fluid',
sources=['fluid']),
#PST_PreStep_1(dest='fluid', sources=['fluid'], dim=2, boundedFlow=self.PST_boundedFlow),
#PST_PreStep_2(dest='fluid', sources=['fluid'], dim=2, H=self.h0, boundedFlow=self.PST_boundedFlow),
],
real=False),
Group(
equations=[
PST(dest='fluid',
sources=['fluid'],
H=self.h0,
dt=self.dt,
dx=self.dx,
Uc0=self.PST_Uc0,
Rh=self.PSR_Rh,
boundedFlow=self.PST_boundedFlow),
ContinuityEquation(dest='fluid', sources=['fluid']),
ContinuityEquationDeltaSPH(dest='fluid',
sources=['fluid'],
c0=self.c0,
delta=0.1),
LaminarViscosityDeltaSPHPreStep(dest='fluid',
sources=['fluid']),
#LaminarViscosity(dest='fluid', sources=['fluid'], nu=self.nu),
LaminarViscosityDeltaSPH(dest='fluid',
sources=['fluid'],
dim=2,
rho0=self.rho0,
nu=self.nu),
Spatial_Acceleration(dest='fluid', sources=['fluid']),
],
real=True),
]
return equations
def get_equations(self):
all = self.fluids + self.solids
stage0 = []
eq1 = []
if self.solids:
for solid in self.solids:
eq1.append(EvaluateNumberDensity(dest=solid, sources=self.fluids))
for fluid in self.fluids:
eq1.append(GradientCorrectionPreStep(dest=fluid, sources=all, dim=self.dim))
eq1.append(GradientCorrection(dest=fluid, sources=all, dim=self.dim))
eq1.append(ContinuityEquationDeltaSPHPreStep(dest=fluid, sources=all))
stage0.append(Group(equations=eq1, real=False))
eq2 = []
for fluid in self.fluids:
eq2.append(ContinuityEquation(dest=fluid, sources=all))
eq2.append(ContinuityEquationDeltaSPH(dest=fluid, sources=all, c0=self.c0))
stage0.append(Group(equations=eq2, real=False))
eq3 = []
for fluid in self.fluids:
eq3.append(IsothermalEOS(dest=fluid, sources=None, rho0=self.rho0, c0=self.c0, p0=0.0))
stage0.append(Group(equations=eq3, real=False))
if self.solids:
eq4 = []
for solid in self.solids:
eq4.append(SetWallVelocity(dest=solid, sources=self.fluids))
eq4.append(SetPressureSolid(dest=solid, sources=self.fluids, rho0=self.rho0, p0=self.p0))
stage0.append(Group(equations=eq4, real=False))
eq5 = []
for fluid in self.fluids:
eq5.append(LaminarViscosityDeltaSPHPreStep(dest=fluid, sources=self.fluids))
eq5.append(LaminarViscosityDeltaSPH(dest=fluid, sources=self.fluids, dim=self.dim, rho0=self.rho0, nu=self.nu))
if self.solids:
eq5.append(SolidWallNoSlipBC(dest=fluid, sources=self.solids, nu=self.nu))
eq5.append(Spatial_Acceleration(dest=fluid, sources=self.fluids))
stage0.append(Group(equations=eq5, real=True))
stage1 = []
eq6 = []
for fluid in self.fluids:
eq6.append(GradientCorrectionPreStep(dest=fluid, sources=all, dim=self.dim))
eq6.append(GradientCorrection(dest=fluid, sources=all, dim=self.dim))
eq6.append(PST_PreStep_1(dest=fluid, sources=all, dim=self.dim, boundedFlow=self.boundedFlow))
eq6.append(PST_PreStep_2(dest=fluid, sources=all, boundedFlow=self.boundedFlow))
stage1.append(Group(equations=eq6, real=False))
eq7 = []
for fluid in self.fluids:
eq7.append(PST(dest=fluid, sources=all, h=self.h0, dt=self.dt, dx=self.dx, c0=self.c0, boundedFlow=self.boundedFlow, gamma=self.gamma))
stage1.append(Group(equations=eq7, real=False))
return MultiStageEquations([stage0,stage1])
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):
# 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 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):
'''
Set-up governing equations
'''
if self.PST == False:
equations = [
Group(equations=[
IsothermalEOS(dest='fluid', sources=['fluid'], rho0=self.rho0, c0=self.c0, p0=0.0),
GradientCorrectionPreStep(dest='fluid', sources=['fluid'], dim=2),
],real=False
),
Group(equations=[
GradientCorrection(dest='fluid', sources=['fluid'], dim=2, tol=0.1),
ContinuityEquationDeltaSPHPreStep(dest='fluid', sources=['fluid']),
],real=True
),
Group(equations=[
ContinuityEquation(dest='fluid', sources=['fluid']),
ContinuityEquationDeltaSPH(dest='fluid', sources=['fluid'], c0=self.c0, delta=0.1),
MomentumEquation(dest='fluid', sources=['fluid'], c0=self.c0, alpha=0.0, beta=0.0, gx=0.0, gy=0.0, gz=0.0, tensile_correction=False),
#MomentumEquationDeltaSPH(dest='fluid', sources=['fluid'], rho0=self.rho0, c0=self.c0, alpha=0.0),
#LaminarViscosityDeltaSPHPreStep(dest='fluid', sources=['fluid']),
LaminarViscosityDeltaSPH(dest='fluid', sources=['fluid'], dim=2, rho0=self.rho0, nu=self.nu),
Spatial_Acceleration(dest='fluid', sources=['fluid']),
#XSPHCorrection(dest='fluid', sources=['fluid'], eps=0.5),
],real=True
),
]
elif self.PST == True:
equations = [
Group(equations=[
IsothermalEOS(dest='fluid', sources=['fluid'], rho0=self.rho0, c0=self.c0, p0=0.0),
GradientCorrectionPreStep(dest='fluid', sources=['fluid'], dim=2),
PST_PreStep_1(dest='fluid', sources=['fluid'], dim=2),
######AverageSpacing(dest='fluid', sources=['fluid'], dim=2),
],real=False
),
Group(equations=[
GradientCorrection(dest='fluid', sources=['fluid'], dim=2, tol=0.1),
ContinuityEquationDeltaSPHPreStep(dest='fluid', sources=['fluid']),
PST_PreStep_2(dest='fluid', sources=['fluid'], dim=2, H=self.h0),
PST(dest='fluid', sources=['fluid'], dim=2, H=self.h0, dt=self.dt, dx=self.dx, Uc0=self.PST_Uc0, Rh=self.PSR_Rh, saveAllDRh=True, R_coeff=self.PST_R_coeff, n_exp=self.PST_n_exp),
],real=True
),
Group(equations=[
ContinuityEquation(dest='fluid', sources=['fluid']),
ContinuityEquationDeltaSPH(dest='fluid', sources=['fluid'], c0=self.c0, delta=0.1),
MomentumEquation(dest='fluid', sources=['fluid'], c0=self.c0, alpha=0.0, beta=0.0, gx=0.0, gy=0.0, gz=0.0, tensile_correction=False),
#MomentumEquationDeltaSPH(dest='fluid', sources=['fluid'], rho0=self.rho0, c0=self.c0, alpha=0.0),
#LaminarViscosityDeltaSPHPreStep(dest='fluid', sources=['fluid']),
LaminarViscosityDeltaSPH(dest='fluid', sources=['fluid'], dim=2, rho0=self.rho0, nu=self.nu),
Spatial_Acceleration(dest='fluid', sources=['fluid']),
#XSPHCorrection(dest='fluid', sources=['fluid'], eps=0.5),
],real=True
),
]
return equations