[docs]
class DeterministicParticleDiffusion(StruphyModel):
"""Diffusion equation discretized with a deterministic particle method.
Parameters
----------
base_units: BaseUnits
Base units for normalization (default: BaseUnits())
"""
@classmethod
def model_type(cls) -> LiteralOptions.ModelTypes:
return "Kinetic"
## species
class Hydrogen(ParticleSpecies):
def __init__(self):
self.var = PICVariable(space="Particles3D")
self.init_variables()
## propagators
class Propagators:
def __init__(self):
self.det_diff = PushDeterministicDiffusion()
## abstract methods
def __init__(self, base_units: BaseUnits = BaseUnits()):
# 0. store input parameters
self.params = copy.deepcopy(locals())
# 1. instantiate all species
self.hydrogen = self.Hydrogen()
# 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.det_diff.variables.var = self.hydrogen.var
# 5. define scalars to be tracked during simulation
@property
def bulk_species(self):
return self.hydrogen
@property
def velocity_scale(self):
return None
def allocate_helpers(self):
pass
[docs]
@classmethod
def doc_pde(cls):
r"""**PDEs solved by model:**
Find :math:`u : \mathbb{R} \times \Omega \to \mathbb{R}^+` such that
.. math::
\frac{\partial u}{\partial t} + \nabla \cdot \left( \mathbf{F}(u) u \right) = 0, \qquad \mathbf{F}(u) = -\mathbb{D} \frac{\nabla u}{u}
where :math:`\mathbb{D} : \Omega \to \mathbb{R}^{3 \times 3}` is a positive diffusion matrix.
At the moment only matrices of the form :math:`D * Id` are implemented, where :math:`D > 0`
is a positive diffusion coefficient.
"""
[docs]
@classmethod
def doc_normalization(cls):
r"""The diffusion coefficient defines the normalization,
.. math::
\hat D = \hat x^2 / \hat t.
No separate plasma velocity scale is used in this model."""
[docs]
@classmethod
def doc_scalar_quantities(cls):
r"""**The following scalars are tracked during simulation:**
- No default scalar diagnostics are defined by this model."""
[docs]
@classmethod
def doc_discretization(cls):
"""Time integration is performed by the following propagators (in sequence):
1. :class:`~struphy.propagators.push_deterministic_diffusion.PushDeterministicDiffusion`
"""
doc = rf"""**1. push_deterministic_diffusion.PushDeterministicDiffusion:**
{PushDeterministicDiffusion.__doc__}
"""
return doc
[docs]
@classmethod
def doc_long_description(cls):
r"""This is a particle discretization of diffusion where particles follow a
deterministic drift derived from the current estimate of the density.
It is intended mainly for diffusion-method development and verification
rather than plasma dynamics."""
[docs]
@classmethod
def doc_examples(cls):
r"""Create and initialize a deterministic diffusion model:
.. code-block:: python
from struphy.models import DeterministicParticleDiffusion
model = DeterministicParticleDiffusion()
model.hydrogen.var
"""
[docs]
@classmethod
def doc_use_cases(cls):
r"""This model is appropriate for:
- deterministic particle discretizations of diffusion
- transport benchmarks with positive scalar densities
- numerical comparison against stochastic diffusion methods"""
[docs]
@classmethod
def doc_cannot_be_used_for(cls):
r"""This model is not suitable for:
- electromagnetic plasma dynamics
- kinetic Vlasov problems in phase space
- nonlinear fluid systems with pressure or momentum evolution
- diffusion tensors outside the currently supported simplified forms"""
