r"""
2D advection diffusion equation for sediment transport.
This can be either conservative :math:`q=HT` or non-conservative :math:`T` sediment and allows
for a separate source and sink term. The equation reads
.. math::
\frac{\partial S}{\partial t}
+ \nabla_h \cdot (\textbf{u} S)
= \nabla_h \cdot (\mu_h \nabla_h S) + F_{source} - (F_{sink} S)
:label: sediment_eq_2d
where :math:`S` is :math:`q` for conservative and :math:`T` for non-conservative,
:math:`\nabla_h` denotes horizontal gradient, :math:`\textbf{u}` are the horizontal
velocities, and :math:`\mu_h` denotes horizontal diffusivity.
"""
from .equation import Equation
from .tracer_eq_2d import HorizontalDiffusionTerm, HorizontalAdvectionTerm, ConservativeHorizontalAdvectionTerm, TracerTerm
__all__ = [
'SedimentEquation2D',
'SedimentTerm',
'ConservativeSedimentAdvectionTerm',
'SedimentAdvectionTerm',
'SedimentErosionTerm',
'SedimentDepositionTerm',
]
[docs]
class SedimentTerm(TracerTerm):
"""
Generic sediment term that provides commonly used members.
"""
def __init__(self, function_space, depth, options, sediment_model, conservative=False):
"""
:arg function_space: :class:`FunctionSpace` where the solution belongs
:arg depth: :class:`DepthExpression` containing depth info
:arg options: :class`ModelOptions2d` containing parameters
:kwarg bool conservative: whether to use conservative tracer
"""
super(SedimentTerm, self).__init__(0, 'sediment_2d', function_space, depth, options)
self.sediment_model = sediment_model
self.conservative = conservative
[docs]
def get_bnd_functions(self, c_in, uv_in, elev_in, bnd_id, bnd_conditions):
funcs = bnd_conditions.get(bnd_id)
c_ext, uv_ext, elev_ext = super().get_bnd_functions(c_in, uv_in, elev_in, bnd_id, bnd_conditions)
if 'equilibrium' in funcs:
if 'value' in funcs:
raise ValueError("Cannot specify both equilibrium and value for sediment bcs.")
c_ext = self.sediment_model.get_equilibrium_tracer()
if self.conservative:
c_ext = c_ext * self.depth.get_total_depth(elev_ext)
return c_ext, uv_ext, elev_ext
[docs]
class ConservativeSedimentAdvectionTerm(SedimentTerm, ConservativeHorizontalAdvectionTerm):
"""
Advection term for sediment equation
Same as :class:`ConservativeHorizontalAdvectionTerm` but allows for equilibrium boundary condition
through get_bnd_conditions() inherited from :class:`SedimentTerm`."""
pass
[docs]
class SedimentAdvectionTerm(SedimentTerm, HorizontalAdvectionTerm):
"""
Advection term for sediment equation
Same as :class:`HorizontalAdvectionTerm` but allows for equilibrium boundary condition
through get_bnd_conditions() inherited from :class:`SedimentTerm`."""
pass
class SedimentDiffusionTerm(SedimentTerm, HorizontalDiffusionTerm):
"""
Diffusion term for sediment equation
Same as :class:`HorizontalDiffusionTerm` but allows for equilibrium boundary condition
through get_bnd_conditions() inherited from :class:`SedimentTerm`."""
pass
[docs]
class SedimentErosionTerm(SedimentTerm):
"""
Erosion term for sediment equation"""
[docs]
def residual(self, solution, solution_old, fields, fields_old, bnd_conditions):
ero = self.sediment_model.get_erosion_term()
if not self.conservative:
elev = fields['elev_2d']
ero = ero / self.depth.get_total_depth(elev)
f = self.test * ero * self.dx
return f
[docs]
class SedimentDepositionTerm(SedimentTerm):
"""
Deposition term for sediment equation"""
[docs]
def residual(self, solution, solution_old, fields, fields_old, bnd_conditions):
depo = self.sediment_model.get_deposition_coefficient()
elev = fields['elev_2d']
H = self.depth.get_total_depth(elev)
f = -self.test * depo/H * solution * self.dx
return f
[docs]
class SedimentEquation2D(Equation):
"""
2D sediment advection-diffusion equation: :eq:`tracer_eq_2d` or :eq:`cons_tracer_eq_2d`
with sediment source and sink term
"""
def __init__(self, function_space, depth, options, sediment_model, conservative=False):
"""
:arg function_space: :class:`FunctionSpace` where the solution belongs
:arg depth: :class:`DepthExpression` containing depth info
:arg options: :class`ModelOptions2d` containing parameters
:kwarg bool conservative: whether to use conservative tracer
"""
super(SedimentEquation2D, self).__init__(function_space)
args = (function_space, depth, options, sediment_model, conservative)
if conservative:
self.add_term(ConservativeSedimentAdvectionTerm(*args), 'explicit')
else:
self.add_term(SedimentAdvectionTerm(*args), 'explicit')
self.add_term(SedimentDiffusionTerm(*args), 'explicit')
self.add_term(SedimentErosionTerm(*args), 'source')
self.add_term(SedimentDepositionTerm(*args), 'implicit')
