[docs]
class VariationalBarotropicFluid(StruphyModel):
"""Barotropic fluid equations discretized with a variational method.
Parameters
----------
base_units: BaseUnits
Base units for normalization (default: BaseUnits())
mass_number: float
Mass number (in units of Proton mass) of the fluid species (default: 1.0)
"""
@classmethod
def model_type(cls) -> LiteralOptions.ModelTypes:
return "Fluid"
## species
class Fluid(FluidSpecies):
def __init__(self, mass_number: float = 1.0):
self.density = FEECVariable(space="L2")
self.velocity = FEECVariable(space="H1vec")
self.init_variables(mass_number=mass_number)
## propagators
class Propagators:
def __init__(self):
self.variat_dens = VariationalDensityEvolve()
self.variat_mom = VariationalMomentumAdvection()
## abstract methods
def __init__(self, base_units: BaseUnits = BaseUnits(), mass_number: float = 1.0):
# 0. store input parameters
self.params = copy.deepcopy(locals())
# 1. instantiate all species
self.fluid = self.Fluid(mass_number=mass_number)
# 2. derive units (must be done after instantiating species to access charge and mass numbers)
self.setup_equation_params(base_units=base_units)
# 3. instantiate all propagators
self.propagators = self.Propagators()
# 4. assign variables to propagators
self.propagators.variat_dens.variables.rho = self.fluid.density
self.propagators.variat_dens.variables.u = self.fluid.velocity
self.propagators.variat_mom.variables.u = self.fluid.velocity
# 5. define scalars to be tracked during simulation
kinetic_energy = BilinearEnergyFEEC(self.fluid.velocity, bilinear_form_name="WMMnew")
thermo_energy = BilinearEnergyFEEC(self.fluid.density)
total_energy = kinetic_energy + thermo_energy
self.scalars = Scalars(
kinetic_energy=kinetic_energy,
thermo_energy=thermo_energy,
total_energy=total_energy,
)
@property
def bulk_species(self):
return self.fluid
@property
def velocity_scale(self):
return "alfvén"
def allocate_helpers(self):
pass
# default parameters
def generate_default_parameter_file(self, path=None, prompt=True):
params_path = super().generate_default_parameter_file(path=path, prompt=prompt)
new_file = []
with open(params_path, "r") as f:
for line in f:
if "variat_dens.Options" in line:
new_file += [
"model.propagators.variat_dens.options = model.propagators.variat_dens.Options(model='barotropic')\n",
]
if "velocity.add_background" in line:
new_file += ["model.fluid.density.add_background(FieldsBackground())\n"]
new_file += [line]
else:
new_file += [line]
with open(params_path, "w") as f:
for line in new_file:
f.write(line)
[docs]
@classmethod
def doc_pde(cls):
r"""**PDEs solved by model:**
Continuity:
.. math::
\partial_t \rho + \nabla \cdot (\rho \mathbf{u}) = 0
Momentum:
.. math::
\partial_t (\rho \mathbf{u}) + \nabla \cdot (\rho \mathbf{u} \otimes \mathbf{u}) + \rho \nabla \frac{(\rho \mathcal{U}(\rho))}{\partial \rho} = 0
where the internal energy per unit mass is :math:`\mathcal U(\rho) = \rho/2`.
"""
[docs]
@classmethod
def doc_normalization(cls):
r"""The reference flow speed is the Alfvén speed and the internal energy is
scaled with density:
.. math::
\hat u = \hat v_A,\qquad \hat{\mathcal U}=\hat\rho/2.
"""
[docs]
@classmethod
def doc_scalar_quantities(cls):
r"""**The following scalars are tracked during simulation:**
- Kinetic energy: ``kinetic_energy``
- Thermodynamic energy: ``thermo_energy``
- Total energy: ``total_energy``"""
[docs]
@classmethod
def doc_discretization(cls):
"""Time integration is performed by the following propagators (in sequence):
1. :class:`~struphy.propagators.variational_density_evolve.VariationalDensityEvolve`
2. :class:`~struphy.propagators.variational_momentum_advection.VariationalMomentumAdvection`
"""
doc = rf"""**1. VariationalDensityEvolve:**
{VariationalDensityEvolve.__doc__}
**2. VariationalMomentumAdvection:**
{VariationalMomentumAdvection.__doc__}
"""
return doc
[docs]
@classmethod
def doc_long_description(cls):
r"""This is the simplest variational compressible-fluid model in Struphy.
It keeps only density and velocity and uses a barotropic closure rather
than a separate entropy or pressure evolution equation."""
[docs]
@classmethod
def doc_examples(cls):
r"""Create and initialize a variational barotropic-fluid model:
.. code-block:: python
from struphy.models import VariationalBarotropicFluid
model = VariationalBarotropicFluid()
model.fluid.density
model.fluid.velocity
"""
[docs]
@classmethod
def doc_use_cases(cls):
r"""This model is appropriate for:
- barotropic compressible-flow benchmarks
- testing variational density and momentum propagators
- reduced fluid studies without entropy evolution"""
[docs]
@classmethod
def doc_cannot_be_used_for(cls):
r"""This model is not suitable for:
- non-barotropic thermodynamics
- magnetic-field dynamics
- viscous or resistive effects
- kinetic plasma phenomena"""
