def test_field_derivative():
f = Frame()
f.addfield("Y", 1.)
f.addintegrationvariable("x", 0.)
def diff(f, x, Y):
return -Y
f.Y.differentiator = diff
with pytest.raises(RuntimeError):
f.Y.derivative()
f.integrator = Integrator(f.x)
f.integrator._var = None
with pytest.raises(RuntimeError):
f.Y.derivative()
f.integrator = Integrator(f.x)
assert np.all(f.Y.derivative() == -f.Y)
f.addfield("Y", [1., 0])
assert np.all(f.Y.derivative() == 0.)
def jac(f, x):
return [[2., 0], [0., 2.]]
f.Y.jacobinator = jac
assert np.all(f.Y.derivative() == [2., 0.])
def test_frame_run():
f = Frame()
f.verbosity = 0
f.addintegrationvariable("x", 0.)
with pytest.raises(RuntimeError):
f.run()
f.integrator = Integrator(f.x)
f.integrator._var = None
with pytest.raises(RuntimeError):
f.run()
f.integrator = Integrator(f.x)
with pytest.raises(RuntimeError):
f.run()
f.x = 3.
f.x.snapshots = [1., 2.]
with pytest.raises(RuntimeError):
f.run()
def dx(f):
return 0.1
f.x.updater = dx
f.x = 1.5
f.run()
assert np.all(f.x == 2.)
def initialize(self):
'''Function initializes the simulation frame.
Function sets all fields that are None with a standard value.
If the grids are not set, it will call ``Simulation.makegrids()`` first.'''
if not isinstance(self.grid.Nm, Field) or not isinstance(self.grid.Nr, Field):
self.makegrids()
# INTEGRATION VARIABLE
if self.t is None:
self.t = IntVar(self, 0., description="Time [s]")
self.t.cfl = 0.1
self.t.updater = std.sim.dt
self.t.snapshots = np.logspace(3., 5., num=21, base=10.) * c.year
# STELLAR QUANTITIES
self._initializestar()
# GRID QUANTITIES
self._initializegrid()
# GAS QUANTITIES
self._initializegas()
# DUST QUANTITIES
self._initializedust()
# INTEGRATOR
if self.integrator is None:
instructions = [
Instruction(std.dust.impl_1_direct,
self.dust.Sigma,
controller={"rhs": self.dust._rhs
},
description="Dust: implicit 1st-order direct solver"
),
Instruction(std.gas.impl_1_direct,
self.gas.Sigma,
controller={"rhs": self.gas._rhs
},
description="Gas: implicit 1st-order direct solver"
),
]
self.integrator = Integrator(
self.t, description="Default integrator")
self.integrator.instructions = instructions
self.integrator.preparator = std.sim.prepare_implicit_dust
self.integrator.finalizer = std.sim.finalize_implicit_dust
# WRITER
if self.writer is None:
self.writer = hdf5writer()
# Updating the entire Simulation object including integrator finalization
self.integrator._finalize()
self.update()
def test_expl_5_cash_karp_adptv():
f = Frame()
f.addfield("Y", 1.)
def dYdx(f, x, Y):
return -Y
f.Y.differentiator = dYdx
f.addintegrationvariable("x", 0.)
def dx(f):
return f.x.suggested
f.x.updater = dx
f.x.snapshots = [10.]
f.x.suggest(0.1)
f.integrator = Integrator(f.x)
f.integrator.instructions = [
Instruction(schemes.expl_5_cash_karp_adptv,
f.Y,
controller={"eps": 1.e-3})
]
f.run()
assert np.allclose(f.Y, 4.57114092616805e-05)
def test_namespacewriter_simple():
f = Frame()
f.addfield("Y", 1.)
f.addgroup("A")
f.A.addfield("B", 0.)
def dYdx(f, x, Y):
return -Y
f.Y.differentiator = dYdx
f.addintegrationvariable("x", 0.)
def dx(f):
return 1.
f.x.updater = dx
f.x.snapshots = [1.]
f.integrator = Integrator(f.x)
f.integrator.instructions = [Instruction(schemes.expl_1_euler, f.Y)]
f.writer = writers.namespacewriter()
f.writer.dumping = True
f.run()
Y = f.writer.read.sequence("Y")
assert np.all(Y == [1., 0.])
x = f.writer.read.sequence("x")
assert np.all(x == [0., 1.])
data = f.writer.read.all()
assert np.all(data.Y == [1., 0.])
assert np.all(data.x == [0., 1.])
f.writer.reset()
def test_expl_2_heun_euler_adaptive():
f = Frame()
f.addfield("Y", 1.)
def dYdx(f, x, Y):
return -Y
f.Y.differentiator = dYdx
f.addintegrationvariable("x", 0.)
def dx(f):
return f.x.suggested
f.x.updater = dx
f.x.snapshots = [10.]
f.x.suggest(0.1)
f.integrator = Integrator(f.x)
f.integrator.instructions = [
Instruction(schemes.expl_2_heun_euler_adptv,
f.Y,
controller={"eps": 1.e-3})
]
f.run()
assert np.allclose(f.Y, 4.553150014598088e-05)
def test_impl_1_euler_gmres_fail():
f = Frame()
f.addfield("Y", 1.)
def jac(f, x):
return np.array([-1.])
f.Y.jacobinator = jac
f.addintegrationvariable("x", 0.)
def dx(f):
return 0.1
f.x.updater = dx
f.x.snapshots = [10.]
f.integrator = Integrator(f.x)
f.integrator.instructions = [
Instruction(schemes.impl_1_euler_gmres,
f.Y,
controller={
"gmres_opt": {
"atol": 0.,
"tol": 1.e-18,
"maxiter": 1
}
})
]
with pytest.raises(StopIteration):
f.run()
def test_expl_3_gottlieb_shu_adptv():
f = Frame()
f.addfield("Y", 1.)
def dYdx(f, x, Y):
return -Y
f.Y.differentiator = dYdx
f.addintegrationvariable("x", 0.)
def dx(f):
return f.x.suggested
f.x.updater = dx
f.x.snapshots = [10.]
f.x.suggest(0.1)
f.integrator = Integrator(f.x)
f.integrator.instructions = [
Instruction(schemes.expl_3_gottlieb_shu_adptv,
f.Y,
controller={"eps": 1.e-4})
]
f.run()
assert np.allclose(f.Y, 4.5390485375346277e-05)
def test_expl_5_dormand_prince_adptv():
f = Frame()
f.addfield("Y", 1.)
def dYdx(f, x, Y):
return -Y
f.Y.differentiator = dYdx
f.addintegrationvariable("x", 0.)
def dx(f):
return f.x.suggested
f.x.updater = dx
f.x.snapshots = [10.]
f.x.suggest(0.1)
f.integrator = Integrator(f.x)
f.integrator.instructions = [
Instruction(schemes.expl_5_dormand_prince_adptv,
f.Y,
controller={"eps": 1.e-2})
]
f.run()
assert np.allclose(f.Y, 1.8016162079480785e-06)
def test_field_jacobian():
f = Frame()
f.addfield("Y", 1.)
f.addintegrationvariable("x", 0.)
def jac(f, x):
if x == None:
return 0.
else:
return x
f.Y.jacobinator = jac
with pytest.raises(RuntimeError):
f.Y.jacobian()
f.integrator = Integrator(f.x)
f.integrator._var = None
with pytest.raises(RuntimeError):
f.Y.jacobian()
f.integrator = Integrator(f.x)
assert f.Y.jacobian() == 0.
assert f.Y.jacobian(x=1.) == 1.
def test_simple_read_files():
f = Frame()
f.addgroup("A")
f.A.addfield("B", [0., 0.])
f.addfield("Y", 1.)
def dYdx(f, x, Y):
return -Y
f.Y.differentiator = dYdx
f.addintegrationvariable("x", 0.)
def dx(f):
return 1.
f.x.updater = dx
f.x.snapshots = [1.]
f.integrator = Integrator(f.x)
f.integrator.instructions = [Instruction(schemes.expl_1_euler, f.Y)]
f.writer = writers.hdf5writer()
f.run()
x = f.writer.read.sequence("x")
assert np.all(x == [0., 1.])
Y = f.writer.read.sequence("Y")
assert np.all(Y == [1., 0.])
B = f.writer.read.sequence("A.B")
assert np.all(B == [0., 0.])
with pytest.raises(TypeError):
f.writer.read.sequence(1)
data = f.writer.read.all()
assert np.all(data.x == [0., 1.])
assert np.all(data.Y == [1., 0.])
assert np.all(data.A.B == [0., 0.])
data0000 = f.writer.read.output(0)
assert np.all(data0000.x == 0.)
assert np.all(data0000.Y == 1.)
assert np.all(data0000.A.B == 0.)
with pytest.raises(RuntimeError):
f.writer.read.output(2)
shutil.rmtree(f.writer.datadir)
with pytest.raises(RuntimeError):
f.writer.datadir = "temp"
f.writer.read.all()
with pytest.raises(RuntimeError):
f.writer.read.sequence("x")
f.writer.datadir = "data"
def test_simple():
f = Frame()
f.addfield("Y", 1.)
def dYdx(f, x, Y):
return -Y
f.Y.differentiator = dYdx
f.addintegrationvariable("x", 0.)
def dx(f):
return 1.
f.x.updater = dx
f.x.snapshots = [1.]
f.integrator = Integrator(f.x)
f.integrator.instructions = [Instruction(schemes.expl_1_euler, f.Y)]
f.run()
assert f.Y == 0.
assert f.x.prevstepsize == 1.
def test_group_repr_str():
f = Frame()
assert isinstance(repr(f), str)
assert isinstance(str(f), str)
f.addintegrationvariable("x", 0)
f.addfield("Y", 1.)
f.addfield("abcdefghijklm", 0.)
f.addgroup("A")
f.addgroup("BCDEFGHIJKLMN")
f.C = None
f.abcdef1234567 = None
f.A.addfield("k", 0.)
assert isinstance(repr(f), str)
assert isinstance(str(f), str)
assert isinstance(repr(f.A), str)
assert isinstance(str(f.A), str)
f.integrator = Integrator(f.x)
f.writer = writers.namespacewriter()
assert isinstance(repr(f), str)
assert isinstance(str(f), str)
def test_expl_4_runge_kutta():
f = Frame()
f.addfield("Y", 1.)
def dYdx(f, x, Y):
return -Y
f.Y.differentiator = dYdx
f.addintegrationvariable("x", 0.)
def dx(f):
return 0.1
f.x.updater = dx
f.x.snapshots = [10.]
f.integrator = Integrator(f.x)
f.integrator.instructions = [Instruction(schemes.expl_4_runge_kutta, f.Y)]
f.run()
assert np.allclose(f.Y, 4.540034101629485e-05)
def test_expl_1_euler():
f = Frame()
f.addfield("Y", 1.)
def dYdx(f, x, Y):
return -Y
f.Y.differentiator = dYdx
f.addintegrationvariable("x", 0.)
def dx(f):
return 0.1
f.x.updater = dx
f.x.snapshots = [10.]
f.integrator = Integrator(f.x)
f.integrator.instructions = [Instruction(schemes.expl_1_euler, f.Y)]
f.run()
assert np.allclose(f.Y, 2.656139888758694e-05)
def test_adaptive_update():
f = Frame()
f.addfield("Y", 1.)
def dYdx(f, x, Y):
return -Y
f.Y.differentiator = dYdx
f.addintegrationvariable("x", 0.)
def dx(f):
return f.x.suggested
f.x.updater = dx
f.x.snapshots = [10.]
f.x.suggest(100.)
f.integrator = Integrator(f.x)
f.integrator.instructions = [Instruction(schemes.expl_5_cash_karp_adptv, f.Y),
Instruction(schemes.update, f.Y)]
f.run()
assert f.Y == 5.34990702474703e-3
def test_expl_2_heun():
f = Frame()
f.addfield("Y", 1.)
def dYdx(f, x, Y):
return -Y
f.Y.differentiator = dYdx
f.addintegrationvariable("x", 0.)
def dx(f):
return 0.1
f.x.updater = dx
f.x.snapshots = [10.]
f.integrator = Integrator(f.x)
f.integrator.instructions = [Instruction(schemes.expl_2_heun, f.Y)]
f.run()
assert np.allclose(f.Y, 4.6222977814657625e-05)
def test_impl_1_euler_gmres():
f = Frame()
f.addfield("Y", 1.)
def jac(f, x):
return np.array([-1.])
f.Y.jacobinator = jac
f.addintegrationvariable("x", 0.)
def dx(f):
return 0.1
f.x.updater = dx
f.x.snapshots = [10.]
f.integrator = Integrator(f.x)
f.integrator.instructions = [Instruction(schemes.impl_1_euler_gmres, f.Y)]
f.run()
assert np.allclose(f.Y, 7.256571590148018e-05)
def test_adaptive_fail():
f = Frame()
f.addfield("Y", 1.)
def dYdx(f, x, Y):
return -Y
f.Y.differentiator = dYdx
f.addintegrationvariable("x", 0.)
def dx(f):
return f.x.suggested
f.x.updater = dx
f.x.snapshots = [10.]
f.x.suggest(100.)
f.integrator = Integrator(f.x)
f.integrator.instructions = [Instruction(
schemes.expl_5_cash_karp_adptv, f.Y)]
f.integrator.maxit = 1
with pytest.raises(StopIteration):
f.run()
def test_impl_2_midpoint_direct():
f = Frame()
f.addfield("Y", 1.)
def jac(f, x):
return np.array([-1.])
f.Y.jacobinator = jac
f.addintegrationvariable("x", 0.)
def dx(f):
return 0.1
f.x.updater = dx
f.x.snapshots = [10.]
f.integrator = Integrator(f.x)
f.integrator.instructions = [
Instruction(schemes.impl_2_midpoint_direct, f.Y)
]
f.run()
assert np.allclose(f.Y, 4.5022605238147066e-05)
def test_integrator_attributes():
f = Frame()
iv = IntVar(f, 0)
i = Integrator(iv)
with pytest.raises(TypeError):
i.description = 1
with pytest.raises(TypeError):
i.maxit = "_"
with pytest.raises(ValueError):
i.maxit = 0
with pytest.raises(TypeError):
i.var = 1
hb = Heartbeat()
i.preparator = hb
assert i.preparator == hb
i.finalizer = hb
assert i.finalizer == hb
i.failop = hb
assert i.failop == hb
with pytest.raises(TypeError):
i.instructions = 1
with pytest.raises(TypeError):
i.instructions = [1]
def test_integrator_repr_str():
f = Frame()
iv = IntVar(f, 0)
i = Integrator(iv)
assert isinstance(repr(i), str)
assert isinstance(str(i), str)
class Simulation(Frame):
"""The main simulation class for running dust coagulation simulations.
`dustpy.Simulation`` is a child of ``simframe.Frame``.
For setting simple initial conditions use ``Simulation.ini``,
For making the simulation grids use ``Simulation.makegrids()``,
For initialization use ``Simulation.initialize()``,
For running simulations use ``Simulation.run()``.
Please have a look at the documentation of ``simframe`` for further details."""
__name__ = "DustPy"
def __init__(self, **kwargs):
"""Main simulation class."""
super().__init__(**kwargs)
# Namespace with parameters to set the initial conditions
self._ini = SimpleNamespace(**{"dust": SimpleNamespace(**{"aIniMax": 0.0001,
"allowDriftingParticles": False,
"erosionMassRatio": 10.,
"d2gRatio": 1.e-2,
"distExp": -3.5,
"excavatedMass": 1.,
"fragmentDistribution": -11/6,
"rhoMonomer": 1.67,
"vfrag": 100.
}
),
"gas": SimpleNamespace(**{"alpha": 1.e-3,
"gamma": 1.4,
"Mdisk": 0.05*c.M_sun,
"mu": 2.3*c.m_p,
"SigmaExp": -1.,
"SigmaRc": 60.*c.au
}
),
"grid": SimpleNamespace(**{"Nmbpd": 7,
"mmin": 1.e-12,
"mmax": 1.e5,
"Nr": 100,
"rmin": 1.*c.au,
"rmax": 1000.*c.au
}
),
"star": SimpleNamespace(**{"M": 1.*c.M_sun,
"R": 2.*c.R_sun,
"T": 5772.,
}
)
}
)
# Initializing everything with None to get the basic frame
# Dust quantities
self.dust = Group(self, description="Dust quantities")
self.dust.a = None
self.dust.backreaction = Group(
self, description="Backreaction coefficients")
self.dust.backreaction.A = None
self.dust.backreaction.B = None
self.dust.backreaction.updater = ["A", "B"]
self.dust.boundary = Group(self, description="Boundary conditions")
self.dust.boundary.inner = None
self.dust.boundary.outer = None
self.dust.coagulation = Group(
self, description="Coagulation quantities")
self.dust.coagulation.stick = None
self.dust.coagulation.stick_ind = None
self.dust.coagulation.A = None
self.dust.coagulation.eps = None
self.dust.coagulation.lf_ind = None
self.dust.coagulation.rm_ind = None
self.dust.coagulation.phi = None
self.dust.D = None
self.dust.delta = Group(self, description="Mixing parameters")
self.dust.delta.rad = None
self.dust.delta.turb = None
self.dust.delta.vert = None
self.dust.delta.updater = ["rad", "turb", "vert"]
self.dust.eps = None
self.dust.Fi = Group(self, description="Fluxes")
self.dust.Fi.adv = None
self.dust.Fi.diff = None
self.dust.Fi.tot = None
self.dust.Fi.updater = ["adv", "diff", "tot"]
self.dust.fill = None
self.dust.H = None
self.dust.kernel = None
self.dust.rho = None
self.dust.rhos = None
self.dust.p = Group(self, description="Probabilities")
self.dust.p.frag = None
self.dust.p.stick = None
self.dust.p.updater = ["frag", "stick"]
self.dust.S = Group(self, description="Sources")
self.dust.S.coag = None
self.dust.S.ext = None
self.dust.S.hyd = None
self.dust.S.tot = None
self.dust.S.updater = ["ext", "tot"]
self.dust.Sigma = None
self.dust.SigmaFloor = None
self.dust.St = None
self.dust.v = Group(self, description="Velocities")
self.dust.v.frag = None
self.dust.v.rel = Group(self, description="Relative velocities")
self.dust.v.rel.azi = None
self.dust.v.rel.brown = None
self.dust.v.rel.rad = None
self.dust.v.rel.tot = None
self.dust.v.rel.turb = None
self.dust.v.rel.vert = None
self.dust.v.rel.updater = [
"azi", "brown", "rad", "turb", "vert", "tot"]
self.dust.v.driftmax = None
self.dust.v.rad = None
self.dust.v.updater = ["frag", "driftmax", "rel"]
self.dust.updater = ["delta", "rhos", "fill", "a", "St", "H",
"rho", "backreaction", "v", "D", "eps", "kernel", "p", "S"]
# Gas quantities
self.gas = Group(self, description="Gas quantities")
self.gas.alpha = None
self.gas.boundary = Group(self, description="Boundary conditions")
self.gas.boundary.inner = None
self.gas.boundary.outer = None
self.gas.cs = None
self.gas.eta = None
self.gas.Fi = None
self.gas.gamma = None
self.gas.Hp = None
self.gas.mfp = None
self.gas.mu = None
self.gas.n = None
self.gas.nu = None
self.gas.P = None
self.gas.rho = None
self.gas.S = Group(self, description="Source terms")
self.gas.S.ext = None
self.gas.S.hyd = None
self.gas.S.tot = None
self.gas.S.updater = ["ext", "tot"]
self.gas.Sigma = None
self.gas.SigmaFloor = None
self.gas.T = None
self.gas.v = Group(self, description="Velocities")
self.gas.v.rad = None
self.gas.v.visc = None
self.gas.v.updater = ["visc", "rad"]
self.gas.updater = ["gamma", "mu", "T", "alpha", "cs", "Hp", "nu",
"rho", "n", "mfp", "P", "eta", "S"]
# Grid quantities
self.grid = Group(self, description="Grid quantities")
self.grid.Nr = None
self.grid.r = None
self.grid.ri = None
self.grid.A = None
self.grid.Nm = None
self.grid.m = None
self.grid.OmegaK = None
self.grid.updater = ["OmegaK"]
# Stellar quantities
self.star = Group(self, description="Stellar quantities")
self.star.L = None
self.star.M = None
self.star.R = None
self.star.T = None
self.star.updater = ["M", "R", "T", "L"]
# Updater of frame object
self.updater = ["star", "grid", "gas", "dust"]
self.t = None
def run(self):
"""This functions runs the simulation."""
# Print welcome message
if self.verbosity > 0:
msg = ""
msg += "\nDustPy v{}".format(self.__version__)
msg += "\n"
msg += "\nDocumentation: {}".format(
"https://stammler.github.io/dustpy/")
msg += "\nPyPI: {}".format(
"https://pypi.org/project/dustpy/")
msg += "\nGitHub: {}".format(
"https://github.com/stammler/dustpy/")
msg += "\n"
msg += colorize("\nPlease cite Stammler & Birnstiel (2022).", "blue")
print(msg)
# Check for mass conserbation
self.checkmassconservation()
# Actually run the simulation
super().run()
@property
def ini(self):
'''Parameter set for setting the initial conditions.'''
return self._ini
def makegrids(self):
'''Function creates radial and mass grid.
Notes
-----
The grids are set up with the parameters given in ``Simulation.ini``.
If you want to have a custom radial grid you have to set the array of grid cell interfaces ``Simulation.grid.ri``,
before calling ``Simulation.makegrids()``.
You cannot have a customized mass grid, because the coagulation alorithm strictly needs a logarithmic grid. Always
set your mass grid parameters with ``Simulation.ini``.'''
self._makemassgrid()
self._makeradialgrid()
def _makemassgrid(self):
'''Function sets the radial mass grid. If ``Simulation.grid.rint`` is not given it uses the parameters set in
``Simulation.ini``.'''
logmmin = np.log10(self.ini.grid.mmin)
logmmax = np.log10(self.ini.grid.mmax)
decades = np.ceil(logmmax - logmmin)
Nm = int(decades * self.ini.grid.Nmbpd) + 1
m = np.logspace(np.log10(self.ini.grid.mmin), np.log10(
self.ini.grid.mmax), num=Nm, base=10.)
self.grid.Nm = Field(
self, Nm, description="# of mass bins", constant=True)
self.grid.m = Field(
self, m, description="Mass grid [g]", constant=True)
def _makeradialgrid(self):
'''Function sets the mass grid using the parameters set in ``Simulation.ini``.'''
if self.grid.ri is None:
ri = np.logspace(np.log10(self.ini.grid.rmin), np.log10(
self.ini.grid.rmax), num=self.ini.grid.Nr+1, base=10.)
Nr = self.ini.grid.Nr
else:
ri = self.grid.ri
Nr = ri.shape[0] - 1
r = 0.5*(ri[:-1] + ri[1:])
A = np.pi*(ri[1:]**2 - ri[:-1]**2)
self.grid.Nr = Field(
self, Nr, description="# of radial grid cells", constant=True)
self.grid.r = Field(
self, r, description="Radial grid cell centers [cm]", constant=True)
self.grid.ri = Field(
self, ri, description="Radial grid cell interfaces [cm]", constant=True)
self.grid.A = Field(
self, A, description="Radial grid annulus area [cm²]", constant=True)
def checkmassconservation(self):
"""Function checks for mass conservation and prints the maximum relative mass error."""
# Check if required fields are present
if self.dust.coagulation.stick is None:
raise RuntimeError(
"'Simulation.dust.coagulation.stick' is not set.")
if self.dust.coagulation.stick_ind is None:
raise RuntimeError(
"'Simulation.dust.coagulation.stick_ind' is not set.")
if self.dust.coagulation.A is None:
raise RuntimeError(
"'Simulation.dust.coagulation.A' is not set.")
if self.dust.coagulation.eps is None:
raise RuntimeError(
"'Simulation.dust.coagulation.eps' is not set.")
if self.dust.coagulation.lf_ind is None:
raise RuntimeError(
"'Simulation.dust.coagulation.lf_ind' is not set.")
if self.dust.coagulation.rm_ind is None:
raise RuntimeError(
"'Simulation.dust.coagulation.rm_ind' is not set.")
if self.dust.coagulation.phi is None:
raise RuntimeError(
"'Simulation.dust.coagulation.phi' is not set.")
if self.grid.m is None:
raise RuntimeError("'sim.grid.m' is not set.")
if self.verbosity > 0:
# Maximum acceptable error
erracc = 1.e-13
# Checking for sticking error
msg = "\n"
msg += colorize("Checking for mass conservation...\n",
color="yellow")
print(msg)
msg = colorize(" - Sticking:", color="yellow")
print(msg)
errmax, i, j = std.dust_f.check_mass_conservation_sticking(
self.dust.coagulation.stick, self.dust.coagulation.stick_ind, self.grid.m)
tup = (j, i)
color = "red"
if(errmax < erracc):
color = "green"
error = "{:9.2e}".format(errmax)
msg = " max. rel. error: {:}\n".format(
colorize(error, color=color))
msg += " for particle collision\n"
msg += " m[{:d}] = {:9.2e} g with\n".format(
tup[0], self.grid.m[tup[0]])
msg += " m[{:d}] = {:9.2e} g".format(
tup[1], self.grid.m[tup[1]])
msg = colorize(msg)
print(msg)
# Checking for full fragmentation error
msg = colorize(" - Full fragmentation:", color="yellow")
print(msg)
A = self.dust.coagulation.A
eps = self.dust.coagulation.eps
klf = self.dust.coagulation.lf_ind
krm = self.dust.coagulation.rm_ind
m = self.grid.m
phi = self.dust.coagulation.phi
errmax, i, j = std.dust_f.check_mass_conservation_full_fragmentation(
A, klf, m, phi)
tup = (j, i)
color = "red"
if(errmax < erracc):
color = "green"
error = "{:9.2e}".format(errmax)
msg = " max. rel. error: {:}\n".format(
colorize(error, color=color))
msg += " for particle collision\n"
msg += " m[{:d}] = {:9.2e} g with\n".format(
tup[0], self.grid.m[tup[0]])
msg += " m[{:d}] = {:9.2e} g".format(
tup[1], self.grid.m[tup[1]])
msg = colorize(msg)
print(msg)
# Checking for erosion error
msg = colorize(" - Erosion:", color="yellow")
print(msg)
errmax, i, j = std.dust_f.check_mass_conservation_erosion(
A, eps, klf, krm, m, phi)
tup = (j, i)
color = "red"
if(errmax < erracc):
color = "green"
error = "{:9.2e}".format(errmax)
msg = " max. rel. error: {:}\n".format(
colorize(error, color=color))
msg += " for particle collision\n"
msg += " m[{:d}] = {:9.2e} g with\n".format(
tup[0], self.grid.m[tup[0]])
msg += " m[{:d}] = {:9.2e} g\n".format(
tup[1], self.grid.m[tup[1]])
msg = colorize(msg)
print(msg)
def initialize(self):
'''Function initializes the simulation frame.
Function sets all fields that are None with a standard value.
If the grids are not set, it will call ``Simulation.makegrids()`` first.'''
if not isinstance(self.grid.Nm, Field) or not isinstance(self.grid.Nr, Field):
self.makegrids()
# INTEGRATION VARIABLE
if self.t is None:
self.t = IntVar(self, 0., description="Time [s]")
self.t.cfl = 0.1
self.t.updater = std.sim.dt
self.t.snapshots = np.logspace(3., 5., num=21, base=10.) * c.year
# STELLAR QUANTITIES
self._initializestar()
# GRID QUANTITIES
self._initializegrid()
# GAS QUANTITIES
self._initializegas()
# DUST QUANTITIES
self._initializedust()
# INTEGRATOR
if self.integrator is None:
instructions = [
Instruction(std.dust.impl_1_direct,
self.dust.Sigma,
controller={"rhs": self.dust._rhs
},
description="Dust: implicit 1st-order direct solver"
),
Instruction(std.gas.impl_1_direct,
self.gas.Sigma,
controller={"rhs": self.gas._rhs
},
description="Gas: implicit 1st-order direct solver"
),
]
self.integrator = Integrator(
self.t, description="Default integrator")
self.integrator.instructions = instructions
self.integrator.preparator = std.sim.prepare_implicit_dust
self.integrator.finalizer = std.sim.finalize_implicit_dust
# WRITER
if self.writer is None:
self.writer = hdf5writer()
# Updating the entire Simulation object including integrator finalization
self.integrator._finalize()
self.update()
def _initializedust(self):
'''Function to initialize dust quantities'''
shape1 = (int(self.grid.Nr))
shape2 = (int(self.grid.Nr), int(self.grid.Nm))
shape2ravel = (int(self.grid.Nr*self.grid.Nm))
shape2p1 = (int(self.grid.Nr)+1, int(self.grid.Nm))
shape3 = (int(self.grid.Nr), int(
self.grid.Nm), int(self.grid.Nm))
# Particle size
if self.dust.a is None:
self.dust.a = Field(self, np.zeros(shape2),
description="Particle size [cm]")
self.dust.a.updater = std.dust.a
# Coagulation parameters
stick, stick_ind, A, eps, lf_ind, rm_ind, phi = std.dust.coagulation_parameters(
self)
if self.dust.coagulation.A is None:
self.dust.coagulation.A = Field(
self, A, description="Fragment normalization factors", constant=True)
if self.dust.coagulation.eps is None:
self.dust.coagulation.eps = Field(
self, eps, description="Remnant mass distribution", constant=True)
if self.dust.coagulation.lf_ind is None:
self.dust.coagulation.lf_ind = Field(
self, lf_ind, description="Index of largest fragment", constant=True)
if self.dust.coagulation.rm_ind is None:
self.dust.coagulation.rm_ind = Field(
self, rm_ind, description="Smaller index of remnant", constant=True)
if self.dust.coagulation.phi is None:
self.dust.coagulation.phi = Field(
self, phi, description="Fragment distribution", constant=True)
if self.dust.coagulation.stick is None:
self.dust.coagulation.stick = Field(
self, stick, description="Sticking matrix", constant=True)
if self.dust.coagulation.stick_ind is None:
self.dust.coagulation.stick_ind = Field(
self, stick_ind, description="Non-zero elements of sticking matrix", constant=True)
# Diffusivity
if self.dust.D is None:
self.dust.D = Field(self, np.zeros(shape2),
description="Diffusivity [cm²/s]")
self.dust.D.updater = std.dust.D
# Deltas
if self.dust.delta.rad is None:
delta = self.ini.gas.alpha * np.ones(shape1)
self.dust.delta.rad = Field(
self, delta, description="Radial mixing parameter")
if self.dust.delta.turb is None:
delta = self.ini.gas.alpha * np.ones(shape1)
self.dust.delta.turb = Field(
self, delta, description="Turbulent mixing parameter")
if self.dust.delta.vert is None:
delta = self.ini.gas.alpha * np.ones(shape1)
self.dust.delta.vert = Field(
self, delta, description="Vertical mixing parameter")
# Vertically integrated dust to gas ratio
if self.dust.eps is None:
self.dust.eps = Field(self, np.zeros(
shape1), description="Dust-to-gas ratio")
self.dust.eps.updater = std.dust.eps
# Fluxes
if self.dust.Fi.adv is None:
self.dust.Fi.adv = Field(self, np.zeros(
shape2p1), description="Advective flux [g/cm/s]")
self.dust.Fi.adv.updater = std.dust.F_adv
if self.dust.Fi.diff is None:
self.dust.Fi.diff = Field(self, np.zeros(
shape2p1), description="Diffusive flux [g/cm/s]")
self.dust.Fi.diff.updater = std.dust.F_diff
if self.dust.Fi.tot is None:
self.dust.Fi.tot = Field(self, np.zeros(
shape2p1), description="Total flux [g/cm/s]")
self.dust.Fi.tot.updater = std.dust.F_tot
# Filling factor
if self.dust.fill is None:
self.dust.fill = Field(self, np.ones(
shape2), description="Filling factor")
# Scale height
if self.dust.H is None:
self.dust.H = Field(self, np.zeros(shape2),
description="Scale heights [cm]")
self.dust.H.updater = std.dust.H
# Kernel
if self.dust.kernel is None:
self.dust.kernel = Field(self, np.zeros(
shape3), description="Collision kernel [cm²/s]")
self.dust.kernel.updater = std.dust.kernel
# Midplane mass density
if self.dust.rho is None:
self.dust.rho = Field(self, np.zeros(
shape2), description="Midplane mass density per mass bin [g/cm³]")
self.dust.rho.updater = std.dust.rho_midplane
# Solid state density
if self.dust.rhos is None:
rhos = self.ini.dust.rhoMonomer * np.ones(shape2)
self.dust.rhos = Field(
self, rhos, description="Solid state density [g/cm³]")
# Probabilities
if self.dust.p.frag is None:
self.dust.p.frag = Field(self, np.zeros(
shape3), description="Fragmentation probability")
self.dust.p.frag.updater = std.dust.p_frag
if self.dust.p.stick is None:
self.dust.p.stick = Field(self, np.zeros(
shape3), description="Sticking probability")
self.dust.p.stick.updater = std.dust.p_stick
# Source terms
if self.dust.S.coag is None:
self.dust.S.coag = Field(self, np.zeros(
shape2), description="Coagulation sources [g/cm²/s]")
self.dust.S.coag.updater = std.dust.S_coag
if self.dust.S.ext is None:
self.dust.S.ext = Field(self, np.zeros(
shape2), description="External sources [g/cm²/s]")
if self.dust.S.hyd is None:
self.dust.S.hyd = Field(self, np.zeros(
shape2), description="Hydrodynamic sources [g/cm²/s]")
self.dust.S.hyd.updater = std.dust.S_hyd
if self.dust.S.tot is None:
self.dust.S.tot = Field(self, np.zeros(
shape2), description="Tot sources [g/cm²/s]")
self.dust.S.tot.updater = std.dust.S_tot
# Stokes number
if self.dust.St is None:
self.dust.St = Field(self, np.zeros(
shape2), description="Stokes number")
self.dust.St.updater = std.dust.St_Epstein_StokesI
# Velocities
if self.dust.v.frag is None:
vfrag = self.ini.dust.vfrag * np.ones(shape1)
self.dust.v.frag = Field(
self, vfrag, description="Fragmentation velocity [cm/s]")
if self.dust.v.rel.azi is None:
self.dust.v.rel.azi = Field(self, np.zeros(
shape3), description="Relative azimuthal velocity [cm/s]")
self.dust.v.rel.azi.updater = std.dust.vrel_azimuthal_drift
if self.dust.v.rel.brown is None:
self.dust.v.rel.brown = Field(self, np.zeros(
shape3), description="Relative Brownian motion velocity [cm/s]")
self.dust.v.rel.brown.updater = std.dust.vrel_brownian_motion
if self.dust.v.rel.rad is None:
self.dust.v.rel.rad = Field(self, np.zeros(
shape3), description="Relative radial velocity [cm/s]")
self.dust.v.rel.rad.updater = std.dust.vrel_radial_drift
if self.dust.v.rel.turb is None:
self.dust.v.rel.turb = Field(self, np.zeros(
shape3), description="Relative turbulent velocity [cm/s]")
self.dust.v.rel.turb.updater = std.dust.vrel_turbulent_motion
if self.dust.v.rel.vert is None:
self.dust.v.rel.vert = Field(self, np.zeros(
shape3), description="Relative vertical settling velocity [cm/s]")
self.dust.v.rel.vert.updater = std.dust.vrel_vertical_settling
if self.dust.v.rel.tot is None:
self.dust.v.rel.tot = Field(self, np.zeros(
shape3), description="Total relative velocity [cm/s]")
self.dust.v.rel.tot.updater = std.dust.vrel_tot
if self.dust.v.driftmax is None:
self.dust.v.driftmax = Field(self, np.zeros(
shape1), description="Maximum drift velocity [cm/s]")
self.dust.v.driftmax.updater = std.dust.vdriftmax
if self.dust.v.rad is None:
self.dust.v.rad = Field(self, np.zeros(
shape2), description="Radial velocity [cm/s]")
self.dust.v.rad.updater = std.dust.vrad
# Initialize dust quantities partly to calculate Sigma
try:
self.dust.update()
except:
pass
# Floor value
if self.dust.SigmaFloor is None:
SigmaFloor = 0.1*std.dust.SigmaFloor(self)
self.dust.SigmaFloor = Field(
self, SigmaFloor, description="Floor value of surface density [g/cm²]")
# Surface density, if not set
if self.dust.Sigma is None:
Sigma = std.dust.MRN_distribution(self)
Sigma = np.where(Sigma <= self.dust.SigmaFloor,
0.1*self.dust.SigmaFloor,
Sigma)
self.dust.Sigma = Field(
self, Sigma, description="Surface density per mass bin [g/cm²]")
self.dust.Sigma.differentiator = std.dust.Sigma_deriv
self.dust.Sigma.jacobinator = std.dust.jacobian
# Fully initialize dust quantities
self.dust.update()
# Hidden fields
# We store the old values of the surface density in a hidden field
# to calculate the fluxes through the boundaries in case of implicit integration.
self.dust._SigmaOld = Field(
self, self.dust.Sigma, description="Previous value of surface density [g/cm²]")
# The right-hand side of the matrix equation is stored in a hidden field
self.dust._rhs = Field(self, np.zeros(
shape2ravel), description="Right-hand side of matrix equation [g/cm²]")
# Boundary conditions
if self.dust.boundary.inner is None:
self.dust.boundary.inner = Boundary(
self.grid.r,
self.grid.ri,
self.dust.Sigma,
condition="const_grad"
)
if self.dust.boundary.outer is None:
self.dust.boundary.outer = Boundary(
self.grid.r[::-1],
self.grid.ri[::-1],
self.dust.Sigma[::-1],
condition="val",
value=0.1*self.dust.SigmaFloor[-1]
)
def _initializegas(self):
'''Function to initialize gas quantities'''
shape1 = (int(self.grid.Nr))
shape1p1 = (int(self.grid.Nr)+1)
# Turbulent alpha parameter
if self.gas.alpha is None:
alpha = self.ini.gas.alpha * np.ones(shape1)
self.gas.alpha = Field(
self, alpha, description="Turbulent alpha parameter")
# Sound speed
if self.gas.cs is None:
self.gas.cs = Field(self, np.zeros(shape1),
description="Sound speed [cm/s]")
self.gas.cs.updater = std.gas.cs_adiabatic
# Pressure gradient parameter
if self.gas.eta is None:
self.gas.eta = Field(self, np.zeros(
shape1), description="Pressure gradient parameter")
self.gas.eta.updater = std.gas.eta_midplane
# Gas flux at the cell interfaces
if self.gas.Fi is None:
self.gas.Fi = Field(self, np.zeros(shape1p1),
description="Gas flux interfaces [g/cm/s]")
self.gas.Fi.updater = std.gas.Fi
# Adiabatic index
if self.gas.gamma is None:
gamma = self.ini.gas.gamma * np.ones(shape1)
self.gas.gamma = Field(self, gamma,
description="Adiabatic index")
# Pressure scale height
if self.gas.Hp is None:
self.gas.Hp = Field(self, np.zeros(shape1),
description="Pressure scale height [cm]")
self.gas.Hp.updater = std.gas.Hp
# Mean free path
if self.gas.mfp is None:
self.gas.mfp = Field(self, np.zeros(shape1),
description="Midplane mean free path [cm]")
self.gas.mfp.updater = std.gas.mfp_midplane
# Mean molecular weight
if self.gas.mu is None:
mu = self.ini.gas.mu * np.ones(shape1)
self.gas.mu = Field(self, mu,
description="Mean molecular weight [g]")
# Midplane number density
if self.gas.n is None:
self.gas.n = Field(self, np.zeros(shape1),
description="Miplane number density [1/cm³]")
self.gas.n.updater = std.gas.n_midplane
# Viscosity
if self.gas.nu is None:
self.gas.nu = Field(self, np.zeros(shape1),
description="Kinematic viscosity [cm²/s]")
self.gas.nu.updater = std.gas.nu
# Midplane pressure
if self.gas.P is None:
self.gas.P = Field(self, np.zeros(shape1),
description="Midplane pressure [g/cm/s²]")
self.gas.P.updater = std.gas.P_midplane
# Midplane mass density
if self.gas.rho is None:
self.gas.rho = Field(self, np.zeros(shape1),
description="Miplane mass density [g/cm³]")
self.gas.rho.updater = std.gas.rho_midplane
# Sources
if self.gas.S.hyd is None:
self.gas.S.hyd = Field(self, np.zeros(
shape1), description="Hydrodynamic sources [g/cm²/s]")
self.gas.S.hyd.updater = std.gas.S_hyd
if self.gas.S.ext is None:
self.gas.S.ext = Field(self, np.zeros(
shape1), description="External sources [g/cm²/s]")
if self.gas.S.tot is None:
self.gas.S.tot = Field(self, np.zeros(
shape1), description="Total sources [g/cm²/s]")
self.gas.S.tot.updater = std.gas.S_tot
# Floor value
if self.gas.SigmaFloor is None:
self.gas.SigmaFloor = Field(
self, 1.e-100*np.ones(shape1), description="Floor value of surface density [g/cm²]")
# Surface density
if self.gas.Sigma is None:
SigmaGas = np.array(std.gas.lyndenbellpringle1974(
self.grid.r, self.ini.gas.SigmaRc, self.ini.gas.SigmaExp, self.ini.gas.Mdisk))
SigmaGas = np.maximum(SigmaGas, self.gas.SigmaFloor)
self.gas.Sigma = Field(self, SigmaGas,
description="Surface density [g/cm²]")
self.gas.Sigma.jacobinator = std.gas.jacobian
# Temperature
if self.gas.T is None:
self.gas.T = Field(self, np.zeros(shape1),
description="Temperature [K]")
self.gas.T.updater = std.gas.T_passive
# Velocities
# Viscous accretion velocity
if self.gas.v.visc is None:
self.gas.v.visc = Field(self, np.zeros(shape1),
description="Viscous accretion velocity [cm/s]")
self.gas.v.visc.updater = std.gas.vvisc
# Radial gas velocity
if self.gas.v.rad is None:
self.gas.v.rad = Field(self, np.zeros(shape1),
description="Radial velocity [cm/s]")
self.gas.v.rad.updater = std.gas.vrad
# Hidden fields
# We store the old values of the surface density in a hidden field
# to calculate the fluxes through the boundaries.
self.gas._SigmaOld = Field(self, np.zeros(
shape1), description="Previous value of surface density [g/cm²]")
self.gas._SigmaOld[:] = self.gas.Sigma
# The right-hand side of the matrix equation is stored in a hidden field
self.gas._rhs = Field(self, np.zeros(
shape1), description="Right-hand side of matrix equation [g/cm²]")
# The dust backreaction coefficients have to be initialized before the gas,
# since the gas velocities need them.
# Backreaction
if self.dust.backreaction.A is None:
self.dust.backreaction.A = Field(
self, np.ones(shape1), description="Pull factor")
if self.dust.backreaction.B is None:
self.dust.backreaction.B = Field(
self, np.zeros(shape1), description="Push factor")
# Initialize gas quantities
self.gas.update()
# Boundary conditions
if self.gas.boundary.inner is None:
self.gas.boundary.inner = Boundary(
self.grid.r, self.grid.ri, self.gas.Sigma)
self.gas.boundary.inner.setcondition("const_grad")
if self.gas.boundary.outer is None:
self.gas.boundary.outer = Boundary(
self.grid.r[::-1], self.grid.ri[::-1], self.gas.Sigma[::-1])
self.gas.boundary.outer.setcondition(
"val", 0.1*self.gas.SigmaFloor[-1])
def _initializegrid(self):
'''Function to initialize grid quantities'''
shape1 = (int(self.grid.Nr))
# Keplerian frequency
if self.grid.OmegaK is None:
self.grid.OmegaK = Field(self, np.zeros(shape1),
description="Keplerian frequency [1/s]")
self.grid.OmegaK.updater = std.grid.OmegaK
# Initialize grid quantities
self.grid.update()
def _initializestar(self):
'''Function to initialize the stellar quantities'''
# Luminosity
if self.star.L is None:
self.star.L = Field(self, 0., description="Luminosity [erg/s]")
self.star.L.updater = std.star.luminosity
# Mass
if self.star.M is None:
self.star.M = Field(self, self.ini.star.M,
description="Mass [g]")
# Radius
if self.star.R is None:
self.star.R = Field(self, self.ini.star.R,
description="Radius [cm]")
# Effective temperature
if self.star.T is None:
self.star.T = Field(self, self.ini.star.T,
description="Effective temperature [K]")
# Initialize stellar quantities
self.star.update()
def setdustintegrator(self, scheme="explicit", method="cash-karp"):
"""Function sets the dust integrator.
Parameters
----------
scheme : string, optional, default : "explicit"
Possible values
{"explicit", "implicit"}
method : string, optional, default : "cash-karp"
Possible values for explicit integration
{"cash-karp"}
Possible values for implicit integration
{"direct", "gmres", "bicgstab}"""
if not isinstance(self.grid.Nm, Field) or not isinstance(self.grid.Nr, Field):
raise RuntimeError(
"The simulation frame has to be initialized before calling setdustimplicit().")
# Get index of dust instruction
for i, inst in enumerate(self.integrator.instructions):
if inst.Y is self.dust.Sigma:
break
if scheme == "implicit":
shape2ravel = (int(self.grid.Nr*self.grid.Nm))
# Hidden fields
# We store the old values of the surface density in a hidden field
# to calculate the fluxes through the boundaries in case of implicit integration.
self.dust._SigmaOld = Field(
self, self.dust.Sigma, description="Previous value of surface density [g/cm²]")
# The right-hand side of the matrix equation is stored in a hidden field
self.dust._rhs = Field(self, np.zeros(
shape2ravel), description="Right-hand side of matrix equation [g/cm²]")
# Setting the Jacobinator
self.dust.Sigma.jacobinator = std.dust.jacobian
# Time step routine
self.t.updater = std.sim.dt
# Updaters
self.dust.v.updater = ["frag", "driftmax", "rel"]
self.dust.updater = ["delta", "rhos", "fill", "a", "St", "H",
"rho", "backreaction", "v", "D", "eps", "kernel", "p", "S"]
self.dust.S.updater = ["ext", "tot"]
# Preparation/Finalization
self.integrator.preparator = std.sim.prepare_implicit_dust
self.integrator.finalizer = std.sim.finalize_implicit_dust
# Integrator
if method == "direct":
inst = Instruction(std.dust.impl_1_direct,
self.dust.Sigma,
controller={"rhs": self.dust._rhs
},
description="Dust: implicit 1st-order direct solver"
)
self.integrator.instructions[i] = inst
elif method == "gmres":
raise NotImplementedError(
"GMRES method is not implemented, yet.")
elif method == "bicgstab":
raise NotImplementedError("BiCGSTAB is not implemented, yet.")
else:
raise RuntimeError("Invalid method for implicit integration.")
elif scheme == "explicit":
# Remove hidden fields if they exist
if hasattr(self.dust, "_SigmaOld"):
del self.dust._SigmaOld
if hasattr(self.dust, "_rhs"):
del self.dust._rhs
# Unset Jacobian
self.dust.Sigma.jacobinator = None
# Updaters
self.dust.v.updater = ["frag", "driftmax", "rad", "rel"]
self.dust.updater = ["delta", "rhos", "fill", "a", "St", "H",
"rho", "backreaction", "v", "D", "eps", "Fi", "kernel", "p", "S"]
self.dust.S.updater = ["coag", "hyd", "ext", "tot"]
# Preparation/Finalization
self.integrator.preparator = std.sim.prepare_explicit_dust
self.integrator.finalizer = std.sim.finalize_explicit_dust
if method == "cash-karp":
# Adaptive time step routine
self.t.updater = std.sim.dt_adaptive
# Instruction
inst = Instruction(schemes.expl_5_cash_karp_adptv,
self.dust.Sigma,
controller={"dYdx": self.dust.S.tot,
"eps": 0.1,
"S": 0.9,
},
description="Dust: explicit 5th-order adaptive Cash-Karp method"
)
self.integrator.instructions[i] = inst
self.t.suggest(1.*c.year)
else:
raise RuntimeError("Invalid method for explicit integration.")
else:
raise RuntimeError("Unknown integration scheme.")
self.integrator._finalize()
self.update()
if self.verbosity > 0:
msg = "Setting dust integrator\n scheme: {}\n method: {}".format(
colorize(scheme, "blue"), colorize(method, "blue"))
print(msg)