def build():
### HOUSEKEEPING: IMPORTANT! ###
inputs = locals().copy()
script = __file__
### INITIALS ###
def apply(system):
curvedBox = CoordSystems.Radial(
system.mesh.radialLengths,
system.mesh.angularExtent,
boxDims=((0., 1.), (0., 1.))).curved_box(system.mesh.data)
initialConditions = InitialConditions.Group([
InitialConditions.Sinusoidal(system.temperatureField.data,
curvedBox),
InitialConditions.Indices(system.temperatureField.data,
[(system.outer.data, 0.),
(system.inner.data, 1.)]),
InitialConditions.SetVal([
system.velocityField.data, system.pressureField.data,
system.temperatureDotField.data
], 0.),
])
initialConditions.apply()
system.solve()
### HOUSEKEEPING: IMPORTANT! ###
return Grouper(locals())
def build(
gradient = 3.,
exponent = 0.5,
smoothness = 10.,
randomSeed = 1066,
):
### HOUSEKEEPING: IMPORTANT! ###
inputs = locals().copy()
script = __file__
### INITIALS ###
def apply(system):
if type(system.mesh) == uw.mesh._spherical_mesh.FeMesh_Annulus:
phase = 1.
curvedBox = CoordSystems.Radial(
system.mesh.radialLengths,
system.mesh.angularExtent,
boxDims = ((0., 1.), (0., 1.))
).curved_box
else:
def curvedBox(argument):
return argument
initialConditions = InitialConditions.Group([
InitialConditions.NoisyGradient(
system.temperatureField.data,
curvedBox(system.mesh.data),
gradient = gradient,
exponent = exponent,
smoothness = smoothness,
randomSeed = randomSeed,
tempRange = (system.surfT, system.baseT),
),
InitialConditions.Indices(
system.temperatureField.data,
[(system.outer.data, system.surfT),
(system.inner.data, system.baseT)]
),
InitialConditions.SetVal(
[system.velocityField.data,
system.pressureField.data,
system.temperatureDotField.data],
0.
),
])
initialConditions.apply()
system.step.value = 0
system.modeltime.value = 0.
system.solve()
### HOUSEKEEPING: IMPORTANT! ###
return Grouper(locals())
def build(obsVars, step, modeltime):
### HOUSEKEEPING: IMPORTANT! ###
# inputs = locals().copy()
inputs = {'obsVars': sorted(obsVars.keys())}
script = __file__
### MAKE STATS ###
statsDict = {}
formatDict = {}
for varName, var in sorted(obsVars.items()):
pevar = planetengine.standardise(var)
var = pevar.var
standardIntegralSuite = {
'surface': ['volume', 'inner', 'outer'],
'comp': ['mag', 'ang', 'rad'],
'gradient': [None, 'ang', 'rad']
}
for inputDict in planetengine.utilities.suite_list(standardIntegralSuite):
anVar = analysis.Analyse.StandardIntegral(
var,
**inputDict
)
statsDict[varName + '_' + anVar.opTag] = anVar
formatDict[varName + '_' + anVar.opTag] = "{:.2f}"
zerodAnalyser = analysis.Analyser(
'zerodData',
statsDict,
formatDict,
step,
modeltime
)
analysers = [zerodAnalyser,] # MAGIC NAME: MUST BE DEFINED
maincollector = analysis.DataCollector(analysers)
collectors = [maincollector,] # MAGIC NAME: MUST BE DEFINED
### FIGS ###
mainfig = visualisation.QuickFig(
*sorted(obsVars.items()),
figname = 'standard'
)
figs = [mainfig,] # MAGIC NAME: MUST BE DEFINED
### HOUSEKEEPING: IMPORTANT! ###
return Grouper(locals())
def make_data(system, step, modeltime):
zerodDataDict = {
'Nu':
analysis.Analyse.DimensionlessGradient(system.temperatureField,
system.mesh,
surfIndexSet=system.outer,
baseIndexSet=system.inner),
'avTemp':
analysis.Analyse.ScalarFieldAverage(system.temperatureField,
system.mesh),
'VRMS':
analysis.Analyse.VectorFieldVolRMS(system.velocityField,
system.mesh),
'surfVRMS':
analysis.Analyse.VectorFieldSurfRMS(system.velocityField,
system.mesh, system.outer),
'avVisc':
analysis.Analyse.ScalarFieldAverage(system.viscosityFn,
system.mesh),
'yielding':
analysis.Analyse.ScalarFieldAverage(
fn.branching.conditional([
(system.creepViscFn < system.plasticViscFn, 0.), (True, 1.)
]), system.mesh),
'step':
analysis.Analyse.ArrayStripper(step, (0, 0)),
'modeltime':
analysis.Analyse.ArrayStripper(modeltime, (0, 0)),
}
zerodFormatDict = {
'Nu': "{:.1f}",
'avTemp': "{:.2f}",
'VRMS': "{:.2f}",
'surfVRMS': "{:.2f}",
'avVisc': "{:.1E}",
'yielding': "{0:.0%}",
'step': "{:.0f}",
'modeltime': "{:.1E}",
}
zerodAnalyser = analysis.Analyser('zerodData', zerodDataDict,
zerodFormatDict)
dataCollector = analysis.DataCollector([
zerodAnalyser,
])
data = {
'analysers': [
zerodAnalyser,
],
'collectors': [
dataCollector,
],
}
return Grouper(data)
def make_tools(system):
viscosityProj = uw.mesh.MeshVariable(system.mesh, 1)
viscosityProjector = uw.utils.MeshVariable_Projection(
viscosityProj,
system.viscosityFn,
)
projectors = {'viscosityProjector': viscosityProjector}
projections = {'viscosityProj': viscosityProj}
tools = {'projectors': projectors, 'projections': projections}
return Grouper(tools)
def build(
pert=0.2,
freq=1.,
phase=0.,
):
### HOUSEKEEPING: IMPORTANT! ###
inputs = locals().copy()
script = __file__
### INITIALS ###
def apply(system):
if type(system.mesh) == uw.mesh._spherical_mesh.FeMesh_Annulus:
phase = 1.
curvedBox = CoordSystems.Radial(system.mesh.radialLengths,
system.mesh.angularExtent,
boxDims=((0., 1.),
(0., 1.))).curved_box
else:
def curvedBox(argument):
return argument
initialConditions = InitialConditions.Group([
InitialConditions.Sinusoidal(system.temperatureField.data,
curvedBox(system.mesh.data),
phase=phase,
freq=freq,
pert=pert,
tempRange=(system.surfT,
system.baseT)),
InitialConditions.Indices(system.temperatureField.data,
[(system.outer.data, system.surfT),
(system.inner.data, system.baseT)]),
InitialConditions.SetVal([
system.velocityField.data, system.pressureField.data,
system.temperatureDotField.data, system.step.value,
system.modeltime.value
], 0.),
])
initialConditions.apply()
system.step.value = 0
system.modeltime.value = 0.
system.solve()
### HOUSEKEEPING: IMPORTANT! ###
return Grouper(locals())
def make_tools(system):
tools = {}
return Grouper(tools)
def build():
### HOUSEKEEPING: IMPORTANT! ###
inputs = locals().copy()
script = __file__
### PROJECTORS ###
def make_tools(system):
tools = {}
return Grouper(tools)
### FIGURES ###
def make_figs(system, tools):
fig = glucifer.Figure(edgecolour="white", quality=2)
figTempComponent = fig.Surface(system.mesh,
system.temperatureField,
colourBar=True)
figVelComponent = fig.VectorArrows(system.mesh, system.velocityField)
figs = {
'fig': fig,
}
return figs
### DATA ###
def make_data(system, tools):
zerodDataDict = {
'Nu':
analysis.Analyse.DimensionlessGradient(
system.temperatureField,
system.mesh,
system.outer,
system.inner,
),
'avTemp':
analysis.Analyse.ScalarFieldAverage(
system.temperatureField,
system.mesh,
),
'VRMS':
analysis.Analyse.VectorFieldVolRMS(
system.velocityField,
system.mesh,
),
'surfVRMS':
analysis.Analyse.VectorFieldSurfRMS(
system.velocityField,
system.mesh,
system.outer,
),
'step':
analysis.Analyse.ArrayStripper(
system.step,
(0, 0),
),
'modeltime':
analysis.Analyse.ArrayStripper(
system.modeltime,
(0, 0),
),
}
zerodFormatDict = {
'Nu': "{:.1f}",
'avTemp': "{:.2f}",
'VRMS': "{:.2f}",
'surfVRMS': "{:.2f}",
'step': "{:.0f}",
'modeltime': "{:.1E}",
}
zerodAnalyser = analysis.Analyser('zerodData', zerodDataDict,
zerodFormatDict)
dataCollector = analysis.DataCollector([
zerodAnalyser,
])
data = {
'analysers': [
zerodAnalyser,
],
'collectors': [
dataCollector,
],
}
return data
### HOUSEKEEPING: IMPORTANT! ###
return Grouper(locals())
def build(
gradient=3.,
exponent=0.5,
smoothness=10.,
randomSeed=1066,
cont_centre=0.5,
cont_width=1. / 3.,
cont_thickness=0.035,
):
### HOUSEKEEPING: IMPORTANT! ###
inputs = locals().copy()
script = __file__
### INITIALS ###
def apply(system):
if type(system.mesh) == uw.mesh._spherical_mesh.FeMesh_Annulus:
phase = 1.
curvedBox = CoordSystems.Radial(system.mesh.radialLengths,
system.mesh.angularExtent,
boxDims=((0., 1.),
(0., 1.))).curved_box
else:
def curvedBox(argument):
return argument
initialConditions = InitialConditions.Group([
InitialConditions.NoisyGradient(
system.temperatureField.data,
curvedBox(system.mesh.data),
gradient=gradient,
exponent=exponent,
smoothness=smoothness,
randomSeed=randomSeed,
tempRange=(system.surfT, system.baseT),
),
InitialConditions.Indices(system.temperatureField.data,
[(system.outer.data, system.surfT),
(system.inner.data, system.baseT)]),
InitialConditions.Extents(
system.materialVar.data,
curvedBox(system.swarm.particleCoordinates.data),
initialExtents=[
(0, fn.misc.constant(True)),
(1,
fn.shape.Polygon(
np.array([[
cont_centre - cont_width / 2., 1. - cont_thickness
], [cont_centre - cont_width / 2., 1.],
[cont_centre + cont_width / 2., 1.],
[
cont_centre + cont_width / 2.,
1. - cont_thickness
]]))),
#(2, fn.shape.Polygon(np.array([[0., 0.], [0., 0.02], [2., 0.02], [2., 0.]]))),
]),
InitialConditions.SetVal([
system.velocityField.data, system.pressureField.data,
system.temperatureDotField.data
], 0.),
])
initialConditions.apply()
system.step.value = 0
system.modeltime.value = 0.
system.solve()
### HOUSEKEEPING: IMPORTANT! ###
return Grouper(locals())
def build(
res=64,
f=0.54,
aspect=1.,
Ra=1e7,
eta0=3e4,
):
### HOUSEKEEPING: IMPORTANT! ###
inputs = locals().copy()
script = __file__
### MESH & MESH VARIABLES ###
maxf = 0.99999
if f == 'max' or f == 1.:
f = maxf
else:
assert f < maxf
length = 1.
outerRad = 1. / (1. - f)
radii = (outerRad - length, outerRad)
maxAspect = math.pi * sum(radii) / length
if aspect == 'max':
aspect = maxAspect
periodic = True
else:
assert aspect < maxAspect
periodic = False
width = length**2 * aspect * 2. / (radii[1]**2 - radii[0]**2)
midpoint = math.pi / 2.
angExtentRaw = (midpoint - 0.5 * width, midpoint + 0.5 * width)
angExtentDeg = [item * 180. / math.pi for item in angExtentRaw]
angularExtent = [
max(0., angExtentDeg[0]),
min(360., angExtentDeg[1] + abs(min(0., angExtentDeg[0])))
]
angLen = angExtentRaw[1] - angExtentRaw[0]
assert res % 4 == 0
radRes = res
angRes = 4 * int(angLen * (int(radRes * radii[1] / length)) / 4)
elementRes = (radRes, angRes)
mesh = uw.mesh.FeMesh_Annulus(elementRes=elementRes,
radialLengths=radii,
angularExtent=angularExtent,
periodic=[False, periodic])
temperatureField = uw.mesh.MeshVariable(mesh, 1)
temperatureDotField = uw.mesh.MeshVariable(mesh, 1)
pressureField = uw.mesh.MeshVariable(mesh.subMesh, 1)
velocityField = uw.mesh.MeshVariable(mesh, 2)
### BOUNDARIES ###
inner = mesh.specialSets["inner"]
outer = mesh.specialSets["outer"]
sides = mesh.specialSets["MaxJ_VertexSet"] + mesh.specialSets[
"MinJ_VertexSet"]
if periodic:
velBC = uw.conditions.RotatedDirichletCondition(
variable=velocityField,
indexSetsPerDof=(inner + outer, None),
basis_vectors=(mesh.bnd_vec_normal, mesh.bnd_vec_tangent))
else:
velBC = uw.conditions.RotatedDirichletCondition(
variable=velocityField,
indexSetsPerDof=(inner + outer, sides),
basis_vectors=(mesh.bnd_vec_normal, mesh.bnd_vec_tangent))
tempBC = uw.conditions.DirichletCondition(variable=temperatureField,
indexSetsPerDof=(inner +
outer, ))
### FUNCTIONS ###
vc = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=2)
vc_eqNum = uw.systems.sle.EqNumber(vc, False)
vcVec = uw.systems.sle.SolutionVector(vc, vc_eqNum)
buoyancyFn = Ra * temperatureField
diffusivityFn = 1.
heatingFn = 1.
### RHEOLOGY ###
viscosityFn = fn.math.pow(eta0, 1. - temperatureField)
### SYSTEMS ###
stokes = uw.systems.Stokes(
velocityField=velocityField,
pressureField=pressureField,
conditions=[
velBC,
],
fn_viscosity=viscosityFn,
fn_bodyforce=buoyancyFn * mesh.unitvec_r_Fn,
_removeBCs=False,
)
solver = uw.systems.Solver(stokes)
advDiff = uw.systems.AdvectionDiffusion(phiField=temperatureField,
phiDotField=temperatureDotField,
velocityField=vc,
fn_diffusivity=diffusivityFn,
fn_sourceTerm=heatingFn,
conditions=[
tempBC,
])
step = fn.misc.constant(0)
modeltime = fn.misc.constant(0.)
### SOLVING ###
def postSolve():
# realign solution using the rotation matrix on stokes
uw.libUnderworld.Underworld.AXequalsY(stokes._rot._cself,
stokes._velocitySol._cself,
vcVec._cself, False)
# remove null space - the solid body rotation velocity contribution
uw.libUnderworld.StgFEM.SolutionVector_RemoveVectorSpace(
stokes._velocitySol._cself, stokes._vnsVec._cself)
def solve():
velocityField.data[:] = 0.
solver.solve(
nonLinearIterate=False,
callback_post_solve=postSolve,
)
uw.libUnderworld.Underworld.AXequalsX(stokes._rot._cself,
stokes._velocitySol._cself,
False)
def integrate():
dt = advDiff.get_max_dt()
advDiff.integrate(dt)
modeltime.value += dt
step.value += 1
def clipVals():
for varName, var in sorted(varsOfState.items()):
varScale = varScales[varName]
inArr = var.data
var.data[:] = np.array([
np.clip(subarr, *clipval)
for subarr, clipval in zip(var.data.T, varScale)
]).T
def iterate():
integrate()
clipVals()
solve()
### HOUSEKEEPING: IMPORTANT! ###
varsOfState = {'temperatureField': temperatureField}
obsVars = {'velocityField': velocityField}
varScales = {'temperatureField': [[0., 1.]]}
varBounds = {'temperatureField': [[0., 1., '.', '.']]}
return Grouper(locals())
def build(
res=32,
ratio=0.5,
aspect=1.,
length=1.,
isoviscous=False,
Ra=1e7,
maxVisc=3e4,
tau0=4e5,
tau1=1e7,
):
### HOUSEKEEPING: IMPORTANT! ###
inputs = locals().copy()
script = __file__
### MESH & MESH VARIABLES ###
outerRad = length / (1. - min(0.99999, max(0.00001, ratio)))
radii = (outerRad - length, outerRad)
width = length**2 * aspect * 2. / (radii[1]**2 - radii[0]**2)
midpoint = math.pi / 2.
angExtentRaw = (midpoint - 0.5 * width, midpoint + 0.5 * width)
angularExtent = [item * 180. / math.pi for item in angExtentRaw]
angLen = angExtentRaw[1] - angExtentRaw[0]
radRes = res
angRes = 4 * int(angLen * (int(radRes * radii[1] / length)) / 4.)
elementRes = (radRes, angRes)
mesh = uw.mesh.FeMesh_Annulus(elementRes=elementRes,
radialLengths=radii,
angularExtent=angularExtent,
periodic=[False, False])
temperatureField = uw.mesh.MeshVariable(mesh, 1)
temperatureDotField = uw.mesh.MeshVariable(mesh, 1)
pressureField = uw.mesh.MeshVariable(mesh.subMesh, 1)
velocityField = uw.mesh.MeshVariable(mesh, 2)
varsOfState = [((("temperatureField", temperatureField), ), ("mesh", mesh))
]
### BOUNDARIES ###
inner = mesh.specialSets["inner"]
outer = mesh.specialSets["outer"]
sides = mesh.specialSets["MaxJ_VertexSet"] + mesh.specialSets[
"MinJ_VertexSet"]
velBC = uw.conditions.RotatedDirichletCondition(
variable=velocityField,
indexSetsPerDof=(inner + outer, sides),
basis_vectors=(mesh.bnd_vec_normal, mesh.bnd_vec_tangent))
tempBC = uw.conditions.DirichletCondition(variable=temperatureField,
indexSetsPerDof=(inner +
outer, ))
### RHEOLOGY ###
vc = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=2)
vc_eqNum = uw.systems.sle.EqNumber(vc, False)
vcVec = uw.systems.sle.SolutionVector(vc, vc_eqNum)
invDensityFn = temperatureField * Ra
buoyancyFn = invDensityFn * mesh.unitvec_r_Fn
if isoviscous:
viscosityFn = creepViscFn = plasticViscFn = 1.
else:
magnitude = fn.math.sqrt(fn.coord()[0]**2 + fn.coord()[1]**2)
depthFn = mesh.radialLengths[1] - magnitude
yieldStressFn = tau0 + (tau1 * depthFn)
secInvFn = fn.tensor.second_invariant(
fn.tensor.symmetric(vc.fn_gradient))
plasticViscFn = yieldStressFn / (2. * secInvFn + 1e-18)
creepViscFn = fn.math.pow(fn.misc.constant(maxVisc),
-1. * (temperatureField - 1.))
viscosityFn = fn.misc.min(
maxVisc, fn.misc.max(1., fn.misc.min(creepViscFn, plasticViscFn)))
### SYSTEMS ###
stokes = uw.systems.Stokes(
velocityField=velocityField,
pressureField=pressureField,
conditions=[
velBC,
],
fn_viscosity=viscosityFn,
fn_bodyforce=buoyancyFn,
_removeBCs=False,
)
solver = uw.systems.Solver(stokes)
advDiff = uw.systems.AdvectionDiffusion(phiField=temperatureField,
phiDotField=temperatureDotField,
velocityField=vc,
fn_diffusivity=1.,
conditions=[
tempBC,
])
### SOLVING ###
def postSolve():
# realign solution using the rotation matrix on stokes
uw.libUnderworld.Underworld.AXequalsY(stokes._rot._cself,
stokes._velocitySol._cself,
vcVec._cself, False)
# remove null space - the solid body rotation velocity contribution
uw.libUnderworld.StgFEM.SolutionVector_RemoveVectorSpace(
stokes._velocitySol._cself, stokes._vnsVec._cself)
def solve():
velocityField.data[:] = 0.
solver.solve(
nonLinearIterate=not isoviscous,
callback_post_solve=postSolve,
)
uw.libUnderworld.Underworld.AXequalsX(stokes._rot._cself,
stokes._velocitySol._cself,
False)
def integrate():
dt = advDiff.get_max_dt()
advDiff.integrate(dt)
return dt
def iterate():
solve()
return integrate()
### HOUSEKEEPING: IMPORTANT! ###
return Grouper(locals())
def build(
res=64,
ratio=0.54,
aspect=1.,
length=1.,
Ra=1e7,
heating=0.,
surfT=0.,
deltaT=1.,
diffusivity=1.,
buoyancy=1.,
creep=1.,
periodic=False,
):
### HOUSEKEEPING: IMPORTANT! ###
inputs = locals().copy()
script = __file__
### MESH & MESH VARIABLES ###
outerRad = length / (1. - min(0.99999, max(0.00001, ratio)))
inputs['ratio'] = ratio
radii = (outerRad - length, outerRad)
maxAspect = math.pi * sum(radii) / length
aspect = min(aspect, maxAspect)
inputs['aspect'] = aspect
if aspect == maxAspect:
periodic = True
inputs['periodic'] = periodic
width = length**2 * aspect * 2. / (radii[1]**2 - radii[0]**2)
midpoint = math.pi / 2.
angExtentRaw = (midpoint - 0.5 * width, midpoint + 0.5 * width)
angExtentDeg = [item * 180. / math.pi for item in angExtentRaw]
angularExtent = [
max(0., angExtentDeg[0]),
min(360., angExtentDeg[1] + abs(min(0., angExtentDeg[0])))
]
angLen = angExtentRaw[1] - angExtentRaw[0]
radRes = max(16, int(res / 16) * 16)
inputs['res'] = radRes
angRes = 16 * int(angLen * (int(radRes * radii[1] / length)) / 16)
elementRes = (radRes, angRes)
mesh = uw.mesh.FeMesh_Annulus(elementRes=elementRes,
radialLengths=radii,
angularExtent=angularExtent,
periodic=[False, periodic])
temperatureField = uw.mesh.MeshVariable(mesh, 1)
temperatureDotField = uw.mesh.MeshVariable(mesh, 1)
pressureField = uw.mesh.MeshVariable(mesh.subMesh, 1)
velocityField = uw.mesh.MeshVariable(mesh, 2)
### BOUNDARIES ###
inner = mesh.specialSets["inner"]
outer = mesh.specialSets["outer"]
sides = mesh.specialSets["MaxJ_VertexSet"] + mesh.specialSets[
"MinJ_VertexSet"]
if periodic:
velBC = uw.conditions.RotatedDirichletCondition(
variable=velocityField,
indexSetsPerDof=(inner + outer, None),
basis_vectors=(mesh.bnd_vec_normal, mesh.bnd_vec_tangent))
else:
velBC = uw.conditions.RotatedDirichletCondition(
variable=velocityField,
indexSetsPerDof=(inner + outer, sides),
basis_vectors=(mesh.bnd_vec_normal, mesh.bnd_vec_tangent))
tempBC = uw.conditions.DirichletCondition(variable=temperatureField,
indexSetsPerDof=(inner +
outer, ))
### FUNCTIONS ###
baseT = surfT + deltaT
buoyancyFn = temperatureField * Ra * mesh.unitvec_r_Fn * buoyancy
diffusivityFn = diffusivity
heatingFn = heating
### RHEOLOGY ###
vc = uw.mesh.MeshVariable(mesh=mesh, nodeDofCount=2)
vc_eqNum = uw.systems.sle.EqNumber(vc, False)
vcVec = uw.systems.sle.SolutionVector(vc, vc_eqNum)
viscosityFn = 1.
### SYSTEMS ###
stokes = uw.systems.Stokes(
velocityField=velocityField,
pressureField=pressureField,
conditions=[
velBC,
],
fn_viscosity=viscosityFn,
fn_bodyforce=buoyancyFn,
_removeBCs=False,
)
solver = uw.systems.Solver(stokes)
advDiff = uw.systems.AdvectionDiffusion(phiField=temperatureField,
phiDotField=temperatureDotField,
velocityField=vc,
fn_diffusivity=diffusivityFn,
fn_sourceTerm=heatingFn,
conditions=[
tempBC,
])
step = fn.misc.constant(0)
modeltime = fn.misc.constant(0.)
### SOLVING ###
def postSolve():
# realign solution using the rotation matrix on stokes
uw.libUnderworld.Underworld.AXequalsY(stokes._rot._cself,
stokes._velocitySol._cself,
vcVec._cself, False)
# remove null space - the solid body rotation velocity contribution
uw.libUnderworld.StgFEM.SolutionVector_RemoveVectorSpace(
stokes._velocitySol._cself, stokes._vnsVec._cself)
def solve():
velocityField.data[:] = 0.
solver.solve(callback_post_solve=postSolve, )
uw.libUnderworld.Underworld.AXequalsX(stokes._rot._cself,
stokes._velocitySol._cself,
False)
def integrate():
dt = advDiff.get_max_dt()
advDiff.integrate(dt)
return dt
def iterate():
solve()
dt = integrate()
modeltime.value += dt
step.value += 1
### HOUSEKEEPING: IMPORTANT! ###
varsOfState = [
(temperatureField, 'temperatureField'),
]
blackhole = [0., 0.]
return Grouper(locals())
def build(
res=32,
isoviscous=False,
aspect=1.,
length=1.,
Ra=1e7,
maxVisc=3e4,
tau0=4e5,
tau1=1e7,
):
### HOUSEKEEPING: IMPORTANT! ###
inputs = locals().copy()
script = __file__
### MESH & MESH VARIABLES ###
elementRes = (res, int(int(4. * res * aspect) / 4))
maxCoord = (aspect, length)
mesh = uw.mesh.FeMesh_Cartesian(elementRes=elementRes, maxCoord=maxCoord)
temperatureField = uw.mesh.MeshVariable(mesh, 1)
temperatureDotField = uw.mesh.MeshVariable(mesh, 1)
pressureField = uw.mesh.MeshVariable(mesh.subMesh, 1)
velocityField = uw.mesh.MeshVariable(mesh, 2)
varsOfState = [((("temperatureField", temperatureField), ), ("mesh", mesh))
]
### BOUNDARIES ###
inner = mesh.specialSets["MinJ_VertexSet"]
outer = mesh.specialSets["MaxJ_VertexSet"]
sides = mesh.specialSets["MaxI_VertexSet"] + mesh.specialSets[
"MinI_VertexSet"]
velBC = uw.conditions.DirichletCondition(
variable=velocityField,
indexSetsPerDof=(sides, inner + outer),
)
tempBC = uw.conditions.DirichletCondition(variable=temperatureField,
indexSetsPerDof=(inner +
outer, ))
### RHEOLOGY ###
invDensityFn = temperatureField * Ra
buoyancyFn = invDensityFn * (0., 1.)
if isoviscous:
viscosityFn = creepViscFn = plasticViscFn = 1.
else:
magnitude = fn.math.sqrt(fn.coord()[0]**2 + fn.coord()[1]**2)
depthFn = mesh.maxCoord[1] - magnitude
yieldStressFn = tau0 + (tau1 * depthFn)
secInvFn = fn.tensor.second_invariant(
fn.tensor.symmetric(velocityField.fn_gradient))
plasticViscFn = yieldStressFn / (2. * secInvFn + 1e-18)
creepViscFn = fn.math.pow(fn.misc.constant(maxVisc),
-1. * (temperatureField - 1.))
viscosityFn = fn.misc.min(
maxVisc, fn.misc.max(1., fn.misc.min(creepViscFn, plasticViscFn)))
### SYSTEMS ###
stokes = uw.systems.Stokes(
velocityField=velocityField,
pressureField=pressureField,
conditions=[
velBC,
],
fn_viscosity=viscosityFn,
fn_bodyforce=buoyancyFn,
_removeBCs=False,
)
solver = uw.systems.Solver(stokes)
advDiff = uw.systems.AdvectionDiffusion(phiField=temperatureField,
phiDotField=temperatureDotField,
velocityField=velocityField,
fn_diffusivity=1.,
conditions=[
tempBC,
])
### SOLVING ###
def solve():
velocityField.data[:] = 0.
solver.solve(nonLinearIterate=not isoviscous, )
def integrate():
dt = advDiff.get_max_dt()
advDiff.integrate(dt)
return dt
def iterate():
solve()
return integrate()
### HOUSEKEEPING: IMPORTANT! ###
return Grouper(locals())
def build():
### HOUSEKEEPING: IMPORTANT! ###
inputs = locals().copy()
script = __file__
### PROJECTORS ###
def make_tools(system):
viscosityProj = uw.mesh.MeshVariable(system.mesh, 1)
viscosityProjector = uw.utils.MeshVariable_Projection(
viscosityProj,
system.viscosityFn,
)
projectors = {'viscosityProjector': viscosityProjector}
projections = {'viscosityProj': viscosityProj}
tools = {'projectors': projectors, 'projections': projections}
return Grouper(tools)
### FIGURES ###
def make_figs(system, tools):
fig = glucifer.Figure(edgecolour="white", quality=2)
figTempComponent = fig.Surface(system.mesh,
system.temperatureField,
colourBar=True)
figVelComponent = fig.VectorArrows(system.mesh, system.velocityField)
figViscComponent = fig.Contours(
system.mesh,
fn.math.log10(tools.projections['viscosityProj']),
colours="red black",
interval=0.5,
colourBar=False,
)
figMaterialComponent = fig.Points(
system.swarm,
fn_colour=system.materialVar,
fn_mask=system.materialVar,
fn_size=4.,
colours="purple",
colourBar=False,
)
figs = {
'fig': fig,
}
return figs
### DATA ###
def make_data(system, tools):
zerodDataDict = {
'Nu':
analysis.Analyse.DimensionlessGradient(
system.temperatureField,
system.mesh,
system.outer,
system.inner,
),
'avTemp':
analysis.Analyse.ScalarFieldAverage(
system.temperatureField,
system.mesh,
),
'VRMS':
analysis.Analyse.VectorFieldVolRMS(
system.velocityField,
system.mesh,
),
'surfVRMS':
analysis.Analyse.VectorFieldSurfRMS(
system.velocityField,
system.mesh,
system.outer,
),
'avVisc':
analysis.Analyse.ScalarFieldAverage(
system.viscosityFn,
system.mesh,
),
'yielding':
analysis.Analyse.ScalarFieldAverage(
fn.branching.conditional([
(system.creepViscFn < system.plasticViscFn, 0.),
(True, 1.),
]), system.mesh),
'step':
analysis.Analyse.ArrayStripper(
system.step,
(0, 0),
),
'modeltime':
analysis.Analyse.ArrayStripper(
system.modeltime,
(0, 0),
),
}
zerodFormatDict = {
'Nu': "{:.1f}",
'avTemp': "{:.2f}",
'VRMS': "{:.2f}",
'surfVRMS': "{:.2f}",
'avVisc': "{:.1E}",
'yielding': "{0:.0%}",
'step': "{:.0f}",
'modeltime': "{:.1E}",
}
zerodAnalyser = analysis.Analyser('zerodData', zerodDataDict,
zerodFormatDict)
dataCollector = analysis.DataCollector([
zerodAnalyser,
])
data = {
'analysers': [
zerodAnalyser,
],
'collectors': [
dataCollector,
],
}
return data
### HOUSEKEEPING: IMPORTANT! ###
return Grouper(locals())
def build():
### HOUSEKEEPING: IMPORTANT! ###
inputs = locals().copy()
script = __file__
### FIGURES ###
def make_figs(system, step, modeltime):
fig = glucifer.Figure(edgecolour="white", quality=2)
figTempComponent = fig.Surface(system.mesh,
system.temperatureField,
colourBar=True)
figVelComponent = fig.VectorArrows(system.mesh, system.velocityField)
figViscComponent = fig.Contours(system.mesh,
fn.math.log10(system.viscosityFn),
colours="red black",
interval=0.5,
colourBar=False)
figs = {
'fig': fig,
}
return figs
### DATA ###
def make_data(system, step, modeltime):
zerodDataDict = {
'Nu':
analysis.Analyse.DimensionlessGradient(system.temperatureField,
system.mesh,
surfIndexSet=system.outer,
baseIndexSet=system.inner),
'avTemp':
analysis.Analyse.ScalarFieldAverage(system.temperatureField,
system.mesh),
'VRMS':
analysis.Analyse.VectorFieldVolRMS(system.velocityField,
system.mesh),
'surfVRMS':
analysis.Analyse.VectorFieldSurfRMS(system.velocityField,
system.mesh, system.outer),
'avVisc':
analysis.Analyse.ScalarFieldAverage(system.viscosityFn,
system.mesh),
'yielding':
analysis.Analyse.ScalarFieldAverage(
fn.branching.conditional([
(system.creepViscFn < system.plasticViscFn, 0.), (True, 1.)
]), system.mesh),
'step':
analysis.Analyse.ArrayStripper(step, (0, 0)),
'modeltime':
analysis.Analyse.ArrayStripper(modeltime, (0, 0)),
}
zerodFormatDict = {
'Nu': "{:.1f}",
'avTemp': "{:.2f}",
'VRMS': "{:.2f}",
'surfVRMS': "{:.2f}",
'avVisc': "{:.1E}",
'yielding': "{0:.0%}",
'step': "{:.0f}",
'modeltime': "{:.1E}",
}
zerodAnalyser = analysis.Analyser('zerodData', zerodDataDict,
zerodFormatDict)
dataCollector = analysis.DataCollector([
zerodAnalyser,
])
data = {
'analysers': [
zerodAnalyser,
],
'collectors': [
dataCollector,
],
}
return Grouper(data)
### HOUSEKEEPING: IMPORTANT! ###
return Grouper(locals())