# -*- coding: utf-8 -*-
"""
@author: Laura C. Kühle
"""
from abc import ABC, abstractmethod
import numpy as np
class Limiter(ABC):
"""Abstract class for limiting function.
Methods
-------
get_name()
Returns string of class name.
apply(projection, cells)
Applies limiting to cells.
"""
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, cells):
"""Applies limiting to cells.
Parameters
----------
projection : ndarray
Matrix of projection for each polynomial degree.
cells : list
Index of cells to limit.
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, cells)
Applies no limiting to cells.
"""
def apply(self, projection, cells):
"""Returns projection without limiting."""
return projection
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, cells)
Applies limiting to cells.
"""
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, cells):
"""Applies limiting to cells.
Parameters
----------
projection : ndarray
Matrix of projection for each polynomial degree.
cells : list
Index of cells to limit.
Returns
-------
new_projection : ndarray
Matrix of updated projection for each polynomial degree.
"""
new_projection = projection.copy()
# If no troubled cells are detected, return copy
if len(cells) == 0:
return new_projection
# Set mask to limit complete projection
cell_slopes = self._set_cell_slope(projection)
modification_mask = self._determine_mask(projection, cell_slopes)
cells = np.array(cells)
mask = np.zeros_like(new_projection, dtype=bool)
mask[self._erase_degree+1:, cells+1] = np.tile(
np.logical_not(modification_mask)[cells],
(len(projection)-self._erase_degree-1, 1))
# Limit troubled cells for higher degrees
new_projection[mask] = 0
return new_projection
def _determine_mask(self, projection, slopes):
"""Determine limiting mask.
Parameters
----------
projection : ndarray
Matrix of projection for each polynomial degree.
slopes : ndarray
Vector of slopes of projection cells.
Returns
-------
ndarray
Mask whether cells should be adjusted.
"""
forward_slopes = (projection[0, 2:]-projection[0, 1:-1]) * (0.5**0.5)
backward_slopes = (projection[0, 1:-1]-projection[0, :-2]) * (0.5**0.5)
pos_mask = np.logical_and(slopes >= 0,
np.logical_and(forward_slopes >= 0,
backward_slopes >= 0))
neg_mask = np.logical_and(slopes <= 0,
np.logical_and(forward_slopes <= 0,
backward_slopes <= 0))
slope_mask = np.logical_or(pos_mask, neg_mask)
return slope_mask
@staticmethod
def _set_cell_slope(projection):
"""Calculates the slope of the cell.
Parameters
----------
projection : ndarray
Matrix of projection for each polynomial degree.
Returns
-------
ndarray
Vector of slopes of projection cells.
"""
root_vector = np.array([np.sqrt(degree+0.5)
for degree in range(len(projection))])
slope = root_vector[1:] @ projection[1:]
return slope[1:-1]
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
----------
threshold : float
Threshold up to which a cell slope does not require limiting.
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
cell_len = config.pop('cell_len')
mod_factor = config.pop('mod_factor', 0)
self._threshold = mod_factor * cell_len**2
def get_name(self):
"""Returns string of class name concatenated with the erase-degree."""
return self.__class__.__name__ + str(self._erase_degree)
def _determine_mask(self, projection, slopes):
"""Determine limiting mask.
Parameters
----------
projection : ndarray
Matrix of projection for each polynomial degree.
slopes : ndarray
Vector of slopes of projection cells.
Returns
-------
ndarray
Mask whether cells should be adjusted.
"""
return np.logical_or(abs(slopes) <= self._threshold,
super()._determine_mask(projection, slopes))