def uOfXT(self,x,t):
if shockSignedDistance(x) < 0:
return -g[2]*(rho_0*(height - x[2])
-(rho_0-rho_1)*smoothedHeaviside_integral(epsFact_density*he,height-waterColumn_z)
+(rho_0-rho_1)*smoothedHeaviside_integral(epsFact_density*he,x[2]-waterColumn_z))
else:
return -rho_1*g[2]
def uOfXT(self,x,t):
if shockSignedDistance(x) < 0:
return -g[2]*(rho_0*(height - x[2])
-(rho_0-rho_1)*smoothedHeaviside_integral(epsFact_density*0.1,height-waterColumn_z)
+(rho_0-rho_1)*smoothedHeaviside_integral(epsFact_density*0.1,x[2]-waterColumn_z))
else:
return -rho_1*g[2]
def twpflowPressure_init(x, t):
p_L = 0.0
phi_L = tank_dim[nd - 1] - waterLevel
phi = x[nd - 1] - waterLevel
return p_L - g[nd - 1] * (rho_0 * (phi_L - phi) + (rho_1 - rho_0) * (
smoothedHeaviside_integral(epsFact_consrv_heaviside * opts.he, phi_L) -
smoothedHeaviside_integral(epsFact_consrv_heaviside * opts.he, phi)))
def p_dirichlet(x,t):
p_L = default_p.L[axis]*rho_air*gravity[axis]
phi_L = default_p.L[axis] - waterLevel
phi = x[axis] - waterLevel
return p_L - gravity[axis]*( rho_water*(phi_L - phi)
+ (rho_air -rho_water)*(smoothedHeaviside_integral(epsFact*he,phi_L)
-smoothedHeaviside_integral(epsFact*he,phi)))
def outflowPressure(x,t):
#return min(L[2] - x[2],L[2]-waterLevel)*rho_1*(-g[2]) + max(waterLevel - x[2],0.0)*rho_0*(-g[2])
p_L = L[2]*rho_1*g[2]
phi_L = L[2] - outflowHeight
phi = x[2] - outflowHeight
return p_L -g[2]*(rho_0*(phi_L - phi)+(rho_1 -rho_0)*(smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi_L)
-smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi)))
def twpflowPressure(x,t):
#return min(L[2] - x[2],L[2]-waterLevel)*rho_1*(-g[2]) + max(waterLevel - x[2],0.0)*rho_0*(-g[2])
p_L = L[2]*rho_1*g[2]
phi_L = wavePhi((x[0],x[1],L[2]),t)
phi = wavePhi(x,t)
return p_L - g[2]*(rho_0*(phi_L - phi)+(rho_1 -rho_0)*(smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi_L)
-smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi)))
def p(x, t):
return -coefficients.g[2] * (
rho_0 * (height - x[2]) -
(rho_0 - rho_1) * smoothedHeaviside_integral(
epsFact_density * he, height - waterLevel) +
(rho_0 - rho_1) * smoothedHeaviside_integral(
epsFact_density * he, x[2] - waterLevel))
def twpflowPressure_init(x, t):
p_L = L[2] * rho_1 * g[2]
phi_L = L[2] - inflowHeightMean
phi = x[2] - inflowHeightMean
return p_L - g[2] * (
rho_0 * (phi_L - phi) + (rho_1 - rho_0) *
(smoothedHeaviside_integral(epsFact_consrv_heaviside * he, phi_L) -
smoothedHeaviside_integral(epsFact_consrv_heaviside * he, phi)))
def outflowPressure(x, t):
p_L = L[2] * rho_1 * g[2]
phi_L = L[2] - outflowHeight
phi = x[2] - outflowHeight
return p_L - g[2] * (
rho_0 * (phi_L - phi) + (rho_1 - rho_0) *
(smoothedHeaviside_integral(epsFact_consrv_heaviside * he, phi_L) -
smoothedHeaviside_integral(epsFact_consrv_heaviside * he, phi)))
def uOfXT(self, x, t):
p_top = 0.0
phi_top = xTop
phi = x[vert_axis] - opts.outlet_level
return p_top - opts.g[vert_axis] * (
opts.rho_0 * (phi_top - phi) + (opts.rho_1 - opts.rho_0) *
(smoothedHeaviside_integral(smoothing, phi_top) -
smoothedHeaviside_integral(smoothing, phi)))
def uOfXT(self, x, t):
p_L = 0.0
phi_L = tank.dim[nd - 1] - water_level
phi = x[nd - 1] - water_level
p = p_L - g[nd - 1] * (rho_0 * (phi_L - phi) + (rho_1 - rho_0) *
(smoothedHeaviside_integral(smoothing, phi_L) -
smoothedHeaviside_integral(smoothing, phi)))
return p
def twpflowPressure(x, t):
p_L = L[2] * rho_1 * g[2]
phi_L = wavePhi((x[0], x[1], L[2]), t)
phi = wavePhi(x, t)
return p_L - g[2] * (
rho_0 * (phi_L - phi) + (rho_1 - rho_0) *
(smoothedHeaviside_integral(epsFact_consrv_heaviside * he, phi_L) -
smoothedHeaviside_integral(epsFact_consrv_heaviside * he, phi)))
def outflowPressure(x, t):
p_L = L[1] * rho_1 * g[1]
phi_L = L[1] - outflowHeight
phi = x[1] - outflowHeight
return p_L - g[1] * (
rho_0 * (phi_L - phi) + (rho_1 - rho_0) *
(smoothedHeaviside_integral(epsFact_density * he, phi_L) -
smoothedHeaviside_integral(epsFact_density * he, phi)))
def smoothedHydrostaticPressure(waterLevel, z):
p_L = L[2] * rho_1 * g[2]
phi = z - waterLevel
phi_L = L[2] - waterLevel
return p_L - g[2] * (
rho_0 * (phi_L - phi) + (rho_1 - rho_0) *
(smoothedHeaviside_integral(epsFact_consrv_heaviside * he, phi_L) -
smoothedHeaviside_integral(epsFact_consrv_heaviside * he, phi)))
def twpflowPressure_init(x, t):
p_L = 0.0
phi_L = tank_dim[nd - 1] - waterLevel
phi = x[nd - 1] - waterLevel
return p_L - g[nd - 1] * (
rho_0 * (phi_L - phi) + (rho_1 - rho_0) *
(smoothedHeaviside_integral(ecH * domain.MeshOptions.he, phi_L) -
smoothedHeaviside_integral(ecH * domain.MeshOptions.he, phi)))
def intwpflowPressure(X, t):
p_top = 0.0
phi_top = topy - waterLevel
phi = X[1] - waterLevel
return p_top - g[1]*(rho_0*(phi_top - phi) + \
(rho_1 -rho_0) * \
(smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi_top)
-
smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi)))
def outtwpflowPressure(X, t):
p_top = 0.0
phi_top = topy - tailwater
phi = X[1] - tailwater
return p_top - g[1]*(rho_0*(phi_top - phi) +
(rho_1 -rho_0) * \
(smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi_top)
-
smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi)))
def hydrostaticPressureOutletWithDepth_p_dirichlet(x, t):
p_top = pRef
phi_top = refLevel - seaLevel
phi = x[vert_axis] - seaLevel
return p_top - g[vert_axis]*(rhoDown*(phi_top - phi) + \
(rhoUp -rhoDown) * \
(smoothedHeaviside_integral(smoothing,phi_top)
-
smoothedHeaviside_integral(smoothing,phi)))
def twpflowPressure(x, t):
#return min(L[2] - x[2],L[2]-waterLevel)*rho_1*(-g[2]) + max(waterLevel - x[2],0.0)*rho_0*(-g[2])
p_L = L[2] * rho_1 * g[2]
phi_L = wavePhi((x[0], x[1], L[2]), t)
phi = wavePhi(x, t)
return p_L - g[2] * (
rho_0 * (phi_L - phi) + (rho_1 - rho_0) *
(smoothedHeaviside_integral(epsFact_consrv_heaviside * he, phi_L) -
smoothedHeaviside_integral(epsFact_consrv_heaviside * he, phi)))
def outflowPressure(x, t):
#return min(L[2] - x[2],L[2]-waterLevel)*rho_1*(-g[2]) + max(waterLevel - x[2],0.0)*rho_0*(-g[2])
p_L = L[2] * rho_1 * g[2]
phi_L = L[2] - outflowHeight
phi = x[2] - outflowHeight
return p_L - g[2] * (
rho_0 * (phi_L - phi) + (rho_1 - rho_0) *
(smoothedHeaviside_integral(epsFact_consrv_heaviside * he, phi_L) -
smoothedHeaviside_integral(epsFact_consrv_heaviside * he, phi)))
def getDBC_p(x,flag):
if altBC:
if flag in [boundaryTags['downstream'],boundaryTags['top']]:
return lambda x,t: -coefficients.g[2]*(rho_0*(inflow_height - x[2])
-(rho_0-rho_1)*smoothedHeaviside_integral(epsFact_density*he,inflow_height-waterLevel)
+(rho_0-rho_1)*smoothedHeaviside_integral(epsFact_density*he,x[2]-waterLevel))
else:
if flag == boundaryTags['downstream']:
return lambda x,t: -coefficients.g[2]*(rho_0*(inflow_height - x[2])
-(rho_0-rho_1)*smoothedHeaviside_integral(epsFact_density*he,inflow_height-waterLevel)
+(rho_0-rho_1)*smoothedHeaviside_integral(epsFact_density*he,x[2]-waterLevel))
def outflowPressure(x, t):
p_L = L[1] * rho_1 * g[1]
phi_L = L[1] - outflowHeight
phi = x[1] - outflowHeight
return p_L - g[1] * (
rho_0 * (phi_L - phi)
+ (rho_1 - rho_0)
* (
smoothedHeaviside_integral(epsFact_density * he, phi_L)
- smoothedHeaviside_integral(epsFact_density * he, phi)
)
)
def twpflowPressure_init(x, t):
p_L = 0.0
phi_L = tank_dim[nd-1] - water_level
phi = x[nd-1] - water_level
return p_L -g[nd-1]*(rho_0*(phi_L - phi)+(rho_1 -rho_0)*(smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi_L)
-smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi)))
def uOfXT(self, x, t):
return 0.0
class PHI_IC:
def uOfXT(self, x, t):
return x[vert_axis]-opts.outlet_level
class VF_IC:
def uOfXT(self, x, t):
return smoothedHeaviside(smoothing,opts.outlet_level-x[vert_axis])
class P_IC:
def uOfXT(self, x, t):
p_top = 0.0
phi_top = xTop
phi = x[vert_axis] - opts.outlet_level
return p_top - opts.g[vert_axis] * (opts.rho_0 * (phi_top - phi) +
(opts.rho_1 - opts.rho_0) *
(smoothedHeaviside_integral(smoothing, phi_top)-
smoothedHeaviside_integral(smoothing, phi)))
initialConditions = {'pressure': P_IC(),
'vel_u': At_Rest(),
'vel_v': At_Rest(),
'vel_w':At_Rest(),
'vof': VF_IC(),
'ncls': PHI_IC(),
'rdls': PHI_IC()}
outputStepping = TpFlow.OutputStepping(final_time=opts.T,
dt_init=opts.dt_init,
dt_output=opts.dt_output,
nDTout=None,
dt_fixed=None)
def p(x,t):
return -coefficients.g[2]*(rho_0*(height - x[2])
-(rho_0-rho_1)*smoothedHeaviside_integral(epsFact_density*he,height-waterLevel)
+(rho_0-rho_1)*smoothedHeaviside_integral(epsFact_density*he,x[2]-waterLevel))
def twpflowPressure_init(x,t):
p_L = L[2]*rho_1*g[2]
phi_L = L[2] - inflowHeightMean
phi = x[2] - inflowHeightMean
return p_L -g[2]*(rho_0*(phi_L - phi)+(rho_1 -rho_0)*(smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi_L)
-smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi)))
def test_hydrostatic_pressure_outlet_with_depth(self):
from proteus.ctransportCoefficients import smoothedHeaviside, smoothedHeaviside_integral
# input
ct = get_context()
b_or = np.array([[0., -1., 0.]])
b_i = 0
seaLevel = 0.5 # m
rhoUp = 1.004e-6 # kg/m3
rhoDown = 1.500e-5 # kg/m3
g = np.array([0., -9.81, 0.]) # m/s2
refLevel = seaLevel
smoothing = 3.*0.01 # m
nd = 2
vert_axis = nd - 1
air = 1.
water = 0.
pRef = 0. # Pa
BC = create_BC(folder='mprans', b_or=b_or, b_i=b_i)
# setting variables
uDir, vDir, wDir, vofDir, pDir, uDiff, kDiff, dissDiff = [],[],[],[],[],[],[],[]
vofCalc, pCalc = [],[]
t_list = get_time_array()
BC.setHydrostaticPressureOutletWithDepth(seaLevel, rhoUp, rhoDown, g, refLevel, smoothing)
# time step iterations
for t in t_list:
x = np.array(get_random_x())
vofDir += [BC.vof_dirichlet.uOfXT(x, t)]
pDir += [BC.p_dirichlet.uOfXT(x, t)]
# Relative system of coordinates based on the point chosen as reference with pressure=pRef
phiCalc = x[vert_axis] - seaLevel
phi_top = refLevel - seaLevel
phi_ref = phi_top - phiCalc
rho_diff = rhoUp - rhoDown
phi_diff = smoothedHeaviside_integral(smoothing, phi_top) - smoothedHeaviside_integral(smoothing, phiCalc)
pTot = pRef - (g[vert_axis]*rhoDown*phi_ref) - (g[vert_axis]*rho_diff*phi_diff)
pCalc += [pTot]
# smoothing for vof activated along either the water-phase and air phase side
if phiCalc <= -smoothing:
Heav = 0.
elif -smoothing < phiCalc < smoothing:
Heav = smoothedHeaviside(smoothing, phiCalc)
else:
Heav = 1.
vofCalc += [Heav*air + (1.-Heav)*water]
# Velocity and turbulence variables
uDir += [BC.u_dirichlet.uOfXT(x, t)]
vDir += [BC.v_dirichlet.uOfXT(x, t)]
wDir += [BC.w_dirichlet.uOfXT(x, t)]
uDiff += [BC.u_diffusive.uOfXT(x, t)]
kDiff += [BC.k_diffusive.uOfXT(x, t)]
dissDiff += [BC.dissipation_diffusive.uOfXT(x, t)]
nt = len(t_list)
uCalc, vCalc, wCalc, uDiffCalc, kCalc, dissCalc = np.zeros(nt), np.zeros(nt), np.zeros(nt), np.zeros(nt), np.zeros(nt), np.zeros(nt)
npt.assert_equal(uDir, uCalc)
npt.assert_equal(vDir, vCalc)
npt.assert_equal(wDir, wCalc)
npt.assert_allclose(pDir, pCalc, atol=1e-10)
npt.assert_equal(vofDir, vofCalc)
npt.assert_equal(uDiff, uDiffCalc)
npt.assert_equal(kDiff, kCalc)
npt.assert_equal(dissDiff, dissCalc)
def outflowPressure(x,t):
p_L = L[2]*rho_1*g[2]
phi_L = L[2] - outflowHeight
phi = x[2] - outflowHeight
return p_L -g[2]*(rho_0*(phi_L - phi)+(rho_1 -rho_0)*(smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi_L)
-smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi)))
def twpflowPressure(x,t):
p_L = L[2]*rho_1*g[2]
phi_L = wavePhi((x[0],x[1],L[2]),t)
phi = wavePhi(x,t)
return p_L -g[2]*(rho_0*(phi_L - phi)+(rho_1 -rho_0)*(smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi_L)
-smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi)))
def test_hydrostatic_pressure_outlet_with_depth(self):
from proteus.ctransportCoefficients import smoothedHeaviside, smoothedHeaviside_integral
# input
ct = get_context()
b_or = np.array([[0., -1., 0.]])
b_i = 0
seaLevel = 0.5 # m
rhoUp = 1.004e-6 # kg/m3
rhoDown = 1.500e-5 # kg/m3
g = np.array([0., -9.81, 0.]) # m/s2
refLevel = seaLevel
smoothing = 3.*0.01 # m
nd = 2
vert_axis = nd - 1
air = 1.
water = 0.
pRef = 0. # Pa
BC = create_BC(folder='mprans', b_or=b_or, b_i=b_i)
# setting variables
uDir, vDir, wDir, vofDir, pDir, uDiff, kDiff, dissDiff = [],[],[],[],[],[],[],[]
vofCalc, pCalc = [],[]
t_list = get_time_array()
BC.setHydrostaticPressureOutletWithDepth(seaLevel, rhoUp, rhoDown, g, refLevel, smoothing)
# time step iterations
for t in t_list:
x = np.array(get_random_x())
vofDir += [BC.vof_dirichlet.uOfXT(x, t)]
pDir += [BC.p_dirichlet.uOfXT(x, t)]
# Relative system of coordinates based on the point chosen as reference with pressure=pRef
phiCalc = x[vert_axis] - seaLevel
phi_top = refLevel - seaLevel
phi_ref = phi_top - phiCalc
rho_diff = rhoUp - rhoDown
phi_diff = smoothedHeaviside_integral(smoothing, phi_top) - smoothedHeaviside_integral(smoothing, phiCalc)
pTot = pRef - (g[vert_axis]*rhoDown*phi_ref) - (g[vert_axis]*rho_diff*phi_diff)
pCalc += [pTot]
# smoothing for vof activated along either the water-phase and air phase side
if phiCalc <= -smoothing:
Heav = 0.
elif -smoothing < phiCalc < smoothing:
Heav = smoothedHeaviside(smoothing, phiCalc)
else:
Heav = 1.
vofCalc += [Heav*air + (1.-Heav)*water]
# Velocity and turbulence variables
uDir += [BC.u_dirichlet.uOfXT(x, t)]
vDir += [BC.v_dirichlet.uOfXT(x, t)]
wDir += [BC.w_dirichlet.uOfXT(x, t)]
uDiff += [BC.u_diffusive.uOfXT(x, t)]
kDiff += [BC.k_diffusive.uOfXT(x, t)]
dissDiff += [BC.dissipation_diffusive.uOfXT(x, t)]
nt = len(t_list)
uCalc, vCalc, wCalc, uDiffCalc, kCalc, dissCalc = np.zeros(nt), np.zeros(nt), np.zeros(nt), np.zeros(nt), np.zeros(nt), np.zeros(nt)
npt.assert_equal(uDir, uCalc)
npt.assert_equal(vDir, vCalc)
npt.assert_equal(wDir, wCalc)
npt.assert_allclose(pDir, pCalc, atol=1e-10)
npt.assert_equal(vofDir, vofCalc)
npt.assert_equal(uDiff, uDiffCalc)
npt.assert_equal(kDiff, kCalc)
npt.assert_equal(dissDiff, dissCalc)
def smoothedHydrostaticPressure(waterLevel,z):
p_L = L[2]*rho_1*g[2]
phi = z - waterLevel
phi_L = L[2] - waterLevel
return p_L -g[2]*(rho_0*(phi_L - phi)+(rho_1 -rho_0)*(smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi_L)
-smoothedHeaviside_integral(epsFact_consrv_heaviside*he,phi)))
def uOfXT(self,x,t):
return -coefficients.g[2]*(rho_0*(inflow_height - x[2])
-(rho_0-rho_1)*smoothedHeaviside_integral(epsFact_density*he,inflow_height-waterLevel)
+(rho_0-rho_1)*smoothedHeaviside_integral(epsFact_density*he,x[2]-waterLevel))
