# -*- coding: utf-8 -*-
"""
@author: Laura C. Kühle
"""
from abc import ABC, abstractmethod
class Limiter(ABC):
"""Abstract class for limiting function.
Methods
-------
get_name()
Returns string of class name.
apply(projection, cell)
Applies limiting to cell.
"""
def __init__(self, config):
"""Initializes Quadrature.
Parameters
----------
config : dict
Additional parameters for limiter.
"""
self._reset(config)
@abstractmethod
def _reset(self, config):
"""Resets instance variables.
Parameters
----------
config : dict
Additional parameters for quadrature.
"""
pass
def get_name(self):
"""Returns string of class name."""
return self.__class__.__name__
@abstractmethod
def apply(self, projection, cell):
"""Applies limiting to cell.
Parameters
----------
projection : ndarray
Matrix of projection for each polynomial degree.
cell: int
Index of cell.
Returns
-------
ndarray
Matrix of updated projection for each polynomial degree.
"""
pass
class NoLimiter(Limiter):
"""Class without any limiting.
Methods
-------
get_name()
Returns string of class name.
apply(projection, cell)
Applies no limiting to cell.
"""
def apply(self, projection, cell):
"""Returns projection of cell without limiting."""
return projection[:, cell]
class MinMod(Limiter):
"""Class for minmod limiting function.
Sets projection for higher degrees to zero when forward backward, and cell
slope values have not the same sign.
Attributes
----------
erase_degree : int
Polynomial degree up to which projection is not set to zero during
limiting.
Methods
-------
get_name()
Returns string of class name.
apply(projection, cell)
Applies limiting to cell.
"""
def _reset(self, config):
"""Resets instance variables.
Parameters
----------
config : dict
Additional parameters for quadrature.
"""
# Unpack necessary configurations
self._erase_degree = config.pop('erase_degree', 0)
def get_name(self):
"""Returns string of class name concatenated with the erase-degree."""
return self.__class__.__name__ + str(self._erase_degree)
def apply(self, projection, cell):
"""Applies limiting to cell.
Parameters
----------
projection : ndarray
Matrix of projection for each polynomial degree.
cell : int
Index of cell.
Returns
-------
adapted_projection : ndarray
Matrix of updated projection for each polynomial degree.
"""
cell_slope = self._set_cell_slope(projection, cell)
is_good_cell = self._determine_modification(projection, cell,
cell_slope)
if is_good_cell:
return projection[:, cell]
adapted_projection = projection[:, cell].copy()
for i in range(len(adapted_projection)):
if i > self._erase_degree:
adapted_projection[i] = 0
return adapted_projection
def _determine_modification(self, projection, cell, cell_slope):
"""Determines whether limiting is applied.
Parameters
----------
projection : ndarray
Matrix of projection for each polynomial degree.
cell : int
Index of cell.
cell_slope : float
Slope of the given cell.
Returns
-------
bool
Flag whether cell should be adjusted.
"""
forward_slope = (projection[0][cell+1]
- projection[0][cell]) * (0.5**0.5)
backward_slope = (projection[0][cell]
- projection[0][cell-1]) * (0.5**0.5)
return (forward_slope <= 0) & (backward_slope <= 0) \
& (cell_slope <= 0) \
| (forward_slope >= 0) & (backward_slope >= 0) & (cell_slope >= 0)
@staticmethod
def _set_cell_slope(projection, cell):
"""Calculates the slope of the cell.
Parameters
----------
projection : ndarray
Matrix of projection for each polynomial degree.
cell : int
Index of cell.
Returns
-------
float
Slope of the given cell.
"""
slope = []
for current_cell in range(len(projection[0])):
new_entry = sum(
projection[degree][current_cell] * (degree+0.5)**0.5
for degree in range(1, len(projection)))
slope.append(new_entry)
return slope[cell]
class ModifiedMinMod(MinMod):
"""Class for modified minmod limiting function.
Sets projection for higher degrees to zero when forward backward, and cell
slope values have not the same sign and cell slope is significantly high.
Attributes
----------
cell_len : float
Length of a cell in mesh.
mod_factor : float
Factor determining whether cell slope is significantly high enough for
modification.
Methods
-------
get_name()
Returns string of class name.
Notes
-----
Also called Cockburn-Shu limiter.
"""
def _reset(self, config):
"""Resets instance variables.
Parameters
----------
config : dict
Additional parameters for quadrature.
"""
super()._reset(config)
# Unpack necessary configurations
self._cell_len = config.pop('cell_len')
self._mod_factor = config.pop('mod_factor', 0)
def get_name(self):
"""Returns string of class name concatenated with the erase-degree."""
return self.__class__.__name__ + str(self._erase_degree)
def _determine_modification(self, projection, cell, cell_slope):
"""Determines whether limiting is applied.
Parameters
----------
projection : ndarray
Matrix of projection for each polynomial degree.
cell : int
Index of cell.
cell_slope : float
Slope of the given cell.
Returns
-------
bool
Flag whether cell should be adjusted.
"""
if abs(cell_slope) <= self._mod_factor*self._cell_len**2:
return True
return super()._determine_modification(projection, cell, cell_slope)