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 __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
# 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]
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
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))
