def construct_eos_for_material(material_tag,units=None,etamin=0.94,etamax=100.0):
"""Return a spheral EOS object for a material identified by tag.
construct_eos_for_material(mtag,units) calls the appropriate spheral eos
constructor for the material identified by mtag, which must be one of the keys
defined in the global shelpers.material_dictionary. This dictionary also
includes additional arguments to be passed to the constructor, when necessary.
The etamin and etamax optional arguments have slightly different meaning
depending on which EOS constructor is actually used. Currently implemented
constructors are:
Tillotson : the value of etamin is passed to the etamin_solid parameter of
the constructor. This is used to limit tensional pressure when
the material is no longer solid. (Note that the spheral
constructor also has an etamin parameter, which is used to
prevent underflows in the pressure computation.)
ANEOS : Not yet implemented.
All pcs runs should use this method to create equations of state, instead of
calling the spheral constructors directly, in order to allow automatic record
keeping of what material was used in a given run. This also allows reusing
"pre cooked" node lists in new runs.
The file <pcs>/MATERIALS.md should contain a table of available material tags.
See also: material_dictionary
"""
# Make sure we are not wasting our time.
assert isinstance(material_tag,str)
assert material_tag.lower() in material_dictionary.keys()
if units is None:
units = sph.PhysicalConstants(1,1,1)
assert isinstance(units,sph.PhysicalConstants)
assert isinstance(etamin,float)
assert isinstance(etamax,float)
# Build eos using our internal dictionary
mat_dict = material_dictionary[material_tag.lower()]
eos_constructor = mat_dict['eos_constructor']
eos_arguments = mat_dict['eos_arguments']
eos = None
if mat_dict['eos_type'] == 'Tillotson':
eos = eos_constructor(eos_arguments['materialName'],
1e-20, 1e20, units,
etamin_solid=etamin)
eos.uid = mat_dict['eos_id']
# Fix for LLNL ignoring the min eta requirement of Tillotson
eos.minimumPressure = eos.pressure(
eos.etamin_solid*eos.referenceDensity, 0)
eos.minimumPressureType = 1 # 0: floor 1: zero
pass
else:
print "EOS type {} not yet implemented".format(mat_dict['eos_type'])
pass
# And Bob's our uncle
return eos
def pflatten_node_list(nl,filename,do_header=True,nl_id=0,silent=False):
"""Flatten physical field values from a node list to a rectangular ascii file.
pflatten_node_list(nl,filename) extracts field variables from all nodes of nl,
which must be a valid node list, and writes them as a rectangular table into
the text file filename. (A short header is also written, using the # comment
character so the resulting file can be easily read with numpy.loadtext.) The
file will be overwritten if it exists. If filename has the .gz extension it
will be compressed using gzip.
pflatten_node_list(...,do_header=False) omits the header and appends the
flattened nl to the end of the file if one exists.
pflatten_node_list(...,nl_id=id) places the integer id in the first column
of every node (row) in the node list. This can be used when appending multiple
lists to the same file, providing a convenient way to distinguish nodes from
different lists when the file is later read. The default id (for single node
list files) is 0.
The format of the output table is (one line per node):
id eos_id x y z vx vy vz m rho p T U hmin hmax
The p in pflatten is for 'parallel', a reminder that all nodes will be
processed in their local rank, without ever being communicated or collected
in a single process. Each mpi rank will wait its turn to access the output
file, so the writing is in fact serial, but avoids bandwidth and memory waste
and is thus suitable for large node lists from high-res runs.
See also: spickle_node_list
"""
# Make sure we are not wasting our time.
assert isinstance(nl,(sph.Spheral.NodeSpace.FluidNodeList3d,
sph.Spheral.SolidMaterial.SolidNodeList3d)
), "argument 1 must be a node list"
assert isinstance(filename, str), "argument 2 must be a simple string"
assert isinstance(do_header, bool), "true or false"
assert isinstance(silent, bool), "true or false"
assert isinstance(nl_id, int), "int only idents"
assert not isinstance(nl_id, bool), "int only idents"
# Determine if file should be compressed.
if os.path.splitext(filename)[1] == '.gz':
import gzip
open = gzip.open
else:
import __builtin__
open = __builtin__.open
# Write the header.
if do_header:
nbGlobalNodes = mpi.allreduce(nl.numInternalNodes, mpi.SUM)
header = header_template.format(nbGlobalNodes)
if mpi.rank == 0:
fid = open(filename,'w')
fid.write(header)
fid.close()
pass
pass
# Start collecting data.
if not silent:
sys.stdout.write('Flattening ' + nl.label() + ' ' + nl.name + '........')
# Get values of field variables stored in internal nodes.
xloc = nl.positions().internalValues()
vloc = nl.velocity().internalValues()
mloc = nl.mass().internalValues()
rloc = nl.massDensity().internalValues()
uloc = nl.specificThermalEnergy().internalValues()
Hloc = nl.Hfield().internalValues()
#(pressure and temperature are stored in the eos object.)
eos = nl.equationOfState()
ploc = sph.ScalarField('ploc',nl)
Tloc = sph.ScalarField('loc',nl)
rref = nl.massDensity()
uref = nl.specificThermalEnergy()
eos.setPressure(ploc,rref,uref)
eos.setTemperature(Tloc,rref,uref)
# Procs take turns writing internal node values to file.
for proc in range(mpi.procs):
if proc == mpi.rank:
fid = open(filename,'a')
for nk in range(nl.numInternalNodes):
line = "{:2d} ".format(nl_id)
line += "{:2d} ".format(getattr(nl,'eos_id',-1))
line += "{0.x:+12.5e} {0.y:+12.5e} {0.z:+12.5e} ".format(xloc[nk])
line += "{0.x:+12.5e} {0.y:+12.5e} {0.z:+12.5e} ".format(vloc[nk])
line += "{0:+12.5e} ".format(mloc[nk])
line += "{0:+12.5e} ".format(rloc[nk])
line += "{0:+12.5e} ".format(ploc[nk])
line += "{0:+12.5e} ".format(Tloc[nk])
line += "{0:+12.5e} ".format(uloc[nk])
line += "{0:+12.5e} ".format(Hloc[nk].Inverse().eigenValues().minElement())
line += "{0:+12.5e} ".format(Hloc[nk].Inverse().eigenValues().maxElement())
line += "\n"
fid.write(line)
pass
fid.close()
pass
mpi.barrier()
pass
# And Bob's our uncle.
if not silent:
print "Done."
def __init__(self, R, eos, rho0=None, rmin=0, units=None, nbins=100):
"""Class constructor for quasi-incompressible density profile.
Assuming a barely compressible, one-layer planet, a pressure profile in
hydrostatic equilibrium can be found by integrating the hydrostatic
equation with constant density. The equation of state can then be inverted
to provide a density profile consistent with this pressure profile.
Although the resulting pressure/density state is not strictly self
consistent, it may be used as a good approximation for small planets that
are not expected to be highly compressed.
This class generates, in the constructor, a density profile: a vector of
radii and a vector of corresponding densities. The __call__ method is used
to extract a density for an arbitrary radius by interpolation. This is to
provide the interface used by some of the existing node generators in
SPHERAL.
Parameters
----------
R : float > 0
Radius of uncompressed planet.
eos : SolidSpheral3d.EquationOfState3d
Equation-of-state of planet material.
rho0 : float > 0, optional
Guess for density at surface. If not provided eos.referenceDensity
will be used.
rMin : float >=0, optional
Bottom of profile to be computed. Default is 0.
units : SolidSpheral3d.PhysicalConstants, optional
Units object if arguments are not in MKS. Must match constants member
of eos. Default is SolidSpheral3d.PhysicalConstants(1,1,1).
nbins : int >= 10, optional
Number of interpolation points in [rMin,R].
"""
# Minimal input checking
assert np.isreal(R) and R > 0
assert np.isreal(rmin) and rmin < R
assert isinstance(eos, sph.EquationOfState3d)
assert type(nbins) is type(1) and nbins >= 10
if rho0 is None:
rho0 = eos.referenceDensity
assert type(rho0) is type(1.0) and rho0 > 0
if units is None:
units = sph.PhysicalConstants(1,1,1)
assert isinstance(units, sph.PhysicalConstants)
assert units.G == eos.constants.G
# Local variables
rvec = np.linspace(rmin, R, num=nbins)
dvec = np.ones(rvec.size)*np.NaN
pvec = np.ones(rvec.size)*np.NaN
# Step one - calculate pressure profile
G = units.G
for k in range(rvec.size):
pvec[k] = 2*np.pi/3*G*rho0**2*(R**2 - rvec[k]**2)
assert np.all(np.isfinite(pvec))
# Step two - lion hunt to invert eos and get a density
def f(x):
return pressure(eos,x,0) - p_hs
for k in range(pvec.size):
p_hs = pvec[k]
x_hi = eos.referenceDensity*2
x_lo = eos.referenceDensity/2
while (x_hi - x_lo) > 1e-12*eos.referenceDensity:
x_hs = (x_lo + x_hi)/2
if f(x_hs) > 0:
x_hi = x_hs
else:
x_lo = x_hs
pass
pass
dvec[k] = x_hs
assert np.all(np.isfinite(dvec))
# Store object data
self.rvec = rvec
self.dvec = dvec
self.pvec = pvec
self.units = units
# And Bob's our uncle.
return
def spickle_node_list(nl,filename=None,silent=False):
"""Pack physical field variables from a node list in a dict and pickle.
(Note: This is not a true pickler class.)
spickle_node_list(nl,filename) extracts field variables from all nodes of nl,
which must be a valid node list, and packs them in a dict that is returned
to the caller. If the optional argument filename is a string then dict will
also be pickled to a file of that name. The file will be overwritten if it
exists.
The s in spickle is for 'serial', a reminder that this method collects all
nodes of the node list (from all ranks) in a single process. Thus this method
is mainly useful for interactive work with small node lists. It is the user's
responsibility to make sure her process has enough memory to hold the returned
dict.
See also: pflatten_node_list
"""
# Make sure we are not wasting our time.
assert isinstance(nl,(sph.Spheral.NodeSpace.FluidNodeList3d,
sph.Spheral.SolidMaterial.SolidNodeList3d)
), "argument 1 must be a node list"
assert isinstance(silent, bool), "true or false"
# Start collecting data.
if not silent:
sys.stdout.write('Pickling ' + nl.label() + ' ' + nl.name + '........')
# Get values of field variables stored in internal nodes.
xloc = nl.positions().internalValues()
vloc = nl.velocity().internalValues()
mloc = nl.mass().internalValues()
rloc = nl.massDensity().internalValues()
uloc = nl.specificThermalEnergy().internalValues()
Hloc = nl.Hfield().internalValues()
#(pressure and temperature are stored in the eos object.)
eos = nl.equationOfState()
ploc = sph.ScalarField('ploc',nl)
Tloc = sph.ScalarField('loc',nl)
rref = nl.massDensity()
uref = nl.specificThermalEnergy()
eos.setPressure(ploc,rref,uref)
eos.setTemperature(Tloc,rref,uref)
# Zip fields so that we have all fields for each node in the same tuple.
# We do this so we can concatenate everything in a single reduction operation,
# to ensure that all fields in one record in the final list belong to the
# same node.
localFields = zip(xloc, vloc, mloc, rloc, uloc, ploc, Tloc, Hloc)
# Do a SUM reduction on all ranks.
# This works because the + operator for python lists is a concatenation!
globalFields = mpi.allreduce(localFields, mpi.SUM)
# Create a dictionary to hold field variables.
nlFieldDict = dict(name=nl.name,
x=[], # position vector
v=[], # velocity vector
m=[], # mass
rho=[], # mass density
p=[], # pressure
h=[], # smoothing ellipsoid axes
T=[], # temperature
U=[], # specific thermal energy
)
# Loop over nodes to fill field values.
nbGlobalNodes = mpi.allreduce(nl.numInternalNodes, mpi.SUM)
for k in range(nbGlobalNodes):
nlFieldDict[ 'x'].append((globalFields[k][0].x, globalFields[k][0].y, globalFields[k][0].z))
nlFieldDict[ 'v'].append((globalFields[k][1].x, globalFields[k][1].y, globalFields[k][1].z))
nlFieldDict[ 'm'].append( globalFields[k][2])
nlFieldDict['rho'].append( globalFields[k][3])
nlFieldDict[ 'U'].append( globalFields[k][4])
nlFieldDict[ 'p'].append( globalFields[k][5])
nlFieldDict[ 'T'].append( globalFields[k][6])
nlFieldDict[ 'h'].append((globalFields[k][7].Inverse().eigenValues().x,
globalFields[k][7].Inverse().eigenValues().y,
globalFields[k][7].Inverse().eigenValues().z,
))
# Optionally, pickle the dict to a file.
if mpi.rank == 0:
if filename is not None:
if isinstance(filename, str):
with open(filename, 'wb') as fid:
pickle.dump(nlFieldDict, fid)
pass
pass
else:
msg = "Dict NOT pickled to file because " + \
"argument 2 is {} instead of {}".format(type(filename), type('x'))
sys.stderr.write(msg+'\n')
pass
pass
pass
# And Bob's our uncle.
if not silent:
print "Done."
return nlFieldDict
def __init__(self, R, rCore, eosMantle, eosCore, nbins = 100, units=None):
"""Class constructor for quasi-incompressible two-layer density profile."""
# Minimal input checking
assert True
if units is None:
units = sph.PhysicalConstants(1,1,1)
assert isinstance(units, sph.PhysicalConstants)
assert units.G == eosMantle.constants.G == eosCore.constants.G
# Local variables
rvec = np.linspace(0, R, num=nbins)
dvec = np.ones(rvec.size)*np.NaN
pvec = np.ones(rvec.size)*np.NaN
rc = rCore
rhoc = eosCore.referenceDensity
rhom = eosMantle.referenceDensity
assert 0 < rc < R
assert rhom <= rhoc
r_inner = rvec[rvec <= rc]
r_outer = rvec[rvec > rc]
# Step one - calculate pressure profile
G = units.G
c2 = 4*np.pi/3*G*(0.5*rhom**2*R**2 - rhom*(rhoc - rhom)*rc**3/R)
c1 = 4*np.pi/3*G*(0.5*rhoc**2 - 1.5*rhom**2 + rhoc*rhom)*rc**2 + c2
p_inner = np.ones(r_inner.size)*np.NaN
p_outer = np.ones(r_outer.size)*np.NaN
for k in range(r_inner.size):
p_inner[k] = c1 - 4*np.pi/3*G*0.5*rhoc**2*r_inner[k]**2
for k in range(r_outer.size):
p_outer[k] = c2 - 4*np.pi/3*G*(0.5*rhom**2*r_outer[k]**2 -
rhom*(rhoc - rhom)*rc**3/r_outer[k])
assert np.all(np.isfinite(p_inner))
assert np.all(np.isfinite(p_outer))
pvec = np.concatenate((p_inner, p_outer))
# Step two - lion hunt to invert eos and get a density
def f(x):
return pressure(eos,x,0) - p_hs
for k in range(rvec.size):
p_hs = pvec[k]
if rvec[k] <= rc:
eos = eosCore
else:
eos = eosMantle
x_hi = eos.referenceDensity*2
x_lo = eos.referenceDensity/2
while (x_hi - x_lo) > 1e-12*eos.referenceDensity:
x_hs = (x_lo + x_hi)/2
if f(x_hs) > 0:
x_hi = x_hs
else:
x_lo = x_hs
pass
pass
dvec[k] = x_hs
assert np.all(np.isfinite(dvec))
# Store object data
self.rvec = rvec
self.dvec = dvec
self.pvec = pvec
self.units = units
# And Bob's our uncle.
return
assert isinstance(eos, sph.EquationOfState3d)
#assert np.isscalar(rho)
#assert np.isscalar(eps)
#assert np.isreal(rho)
#assert np.isreal(eps)
# Assign thermo values to fields and calculate pressure
pressure.rhof[0] = rho
pressure.epsf[0] = eps
eos.setPressure(pressure.peef, pressure.rhof, pressure.epsf)
# Extract pressure from field and return
return pressure.peef[0]
# End function pressure
# Static fake node list and thermo fields for function pressure
pressure.nodes = sph.makeVoidNodeList('fakenodes',1)
pressure.rhof = sph.ScalarField('rho',pressure.nodes)
pressure.epsf = sph.ScalarField('eps',pressure.nodes)
pressure.peef = sph.ScalarField('pee',pressure.nodes)
class HydrostaticQIC1LayerDensityProfile():
"""Callable hydrostatic quasi-incompressible density profile."""
#---------------------------------------------------------------------------
# The constructor
#---------------------------------------------------------------------------
def __init__(self, R, eos, rho0=None, rmin=0, units=None, nbins=100):
"""Class constructor for quasi-incompressible density profile.
Assuming a barely compressible, one-layer planet, a pressure profile in
hydrostatic equilibrium can be found by integrating the hydrostatic
# currently used by pcs into the global workspace. There you can interactively
# call the EOS methods and compare different materials. This script can also be
# used to extract the code snippets needed to create EOS objects in spheral runs.
#-------------------------------------------------------------------------------
import sys, os
import SolidSpheral3d as sph # The top-level spheral module importer
#-------------------------------------------------------------------------------
# Setup
#-------------------------------------------------------------------------------
# Show signs of life.
print "Loading spheral equations of state..."
# EOS constructors take a units object. I usually work in MKS.
units = sph.PhysicalConstants(1.0, # Unit length in meters
1.0, # Unit mass in kg
1.0) # Unit time in seconds
#-------------------------------------------------------------------------------
# Tillotson EOS for common materials
#-------------------------------------------------------------------------------
mats = ['Granite', 'Basalt', 'Nylon', 'Pure Ice', '30% Silicate Ice', 'Water']
etamin, etamax = 0.94, 10.0
pext, pmin, pmax = 0.0, -1e200, 1e200 # these are actually the defaults
EOSes = [sph.TillotsonEquationOfState(mat, 1e-20, 1e20, units,
etamin_solid = etamin,
externalPressure = pext, minimumPressure = pmin, maximumPressure = pmax)
for mat in mats]
granite = EOSes[0]
basalt = EOSes[1]
nylon = EOSes[2]
import mpi # Mike's simplified mpi wrapper
import SolidSpheral3d as sph # The top-level spheral module importer
from GenerateNodeDistribution3d import GenerateNodeDistribution3d # basic nl-gens
from VoronoiDistributeNodes import distributeNodes3d # the load distributer
pcsbase = '' # Edit this with full path to <pcs> if you see an ImportError.
sys.path += ['..', pcsbase, os.getenv('PCSBASE', '')]
import shelpers # My module of some helper functions
#-------------------------------------------------------------------------------
# Construct a minimal spheral simulation structure, consisting of a node list, a
# node lists generator, a node list distributer, a physics package, an integrator,
# and a controller.
#-------------------------------------------------------------------------------
# First, create an equation of state.
units = sph.PhysicalConstants(1.0, 1.0, 1.0)
eos = shelpers.construct_eos_for_material('h2oice', units)
# Create an empty node list.
nodes = sph.makeFluidNodeList('nodelist', eos)
# Create a stock generator.
generator = GenerateNodeDistribution3d(2,
2,
2,
eos.referenceDensity,
distributionType='lattice')
# Distribute nodes to ranks (suppress with any cl arg to speed things up).
if len(sys.argv) == 1:
distributeNodes3d((nodes, generator))
pcsbase = '' # Edit this with full path to <pcs> if you see an ImportError.
sys.path += ['..',pcsbase,os.getenv('PCSBASE','')]
import shelpers # My module of some helper functions
#-------------------------------------------------------------------------------
# Construct a minimal spheral simulation structure, consisting of a node list, a
# node lists generator, a node list distributer, a physics package, an integrator,
# and a controller.
#-------------------------------------------------------------------------------
# First, create an equation of state.
units = sph.PhysicalConstants(1.0,1.0,1.0)
eos = shelpers.construct_eos_for_material('h2oice',units)
# Create an empty node list.
nodes = sph.makeFluidNodeList('nodelist', eos)
# Create a stock generator.
generator = GenerateNodeDistribution3d(2, 2, 2,
eos.referenceDensity,
distributionType = 'lattice')
# Distribute nodes to ranks (suppress with any cl arg to speed things up).
if len(sys.argv) == 1:
distributeNodes3d((nodes, generator))
# Create a DataBase object to hold the node lists.
db = sph.DataBase()
db.appendNodeList(nodes)
# Create the kernel function for SPH.
