# -*- coding: utf-8 -*-
"""
@author: Laura C. Kühle
"""
from abc import ABC, abstractmethod
import time
from .Equation import Equation
class UpdateScheme(ABC):
"""Abstract class for updating projections at a time step.
Methods
-------
get_name()
Returns string of class name.
step(projection, cfl_number)
Performs time step.
"""
def __init__(self, detector, limiter, equation):
"""Initializes UpdateScheme.
Parameters
----------
detector : TroubledCellDetector object
Troubled cell detector for evaluation.
limiter : Limiter object
Limiter for evaluation.
equation: Equation
Equation.
"""
# Unpack positional arguments
self._detector = detector
self._limiter = limiter
self._equation = equation
self._reset()
def _reset(self):
"""Resets instance variables."""
def get_name(self):
"""Returns string of class name."""
return self.__class__.__name__
def step(self, projection, cfl_number):
"""Performs time step.
Parameters
----------
projection : ndarray
Matrix of projection for each polynomial degree.
cfl_number : float
CFL number to ensure stability.
Returns
-------
current_projection : ndarray
Matrix of projection of current update step for each polynomial
degree.
troubled_cells : list
List of indices for all detected troubled cells.
"""
current_projection, troubled_cells = self._apply_stability_method(
projection, cfl_number)
return current_projection, troubled_cells
@abstractmethod
def _apply_stability_method(self, projection, cfl_number):
"""Applies stability method.
Parameters
----------
projection : ndarray
Matrix of projection for each polynomial degree.
cfl_number : float
CFL number to ensure stability.
Returns
-------
current_projection : ndarray
Matrix of projection of current update step for each polynomial
degree.
troubled_cells : list
List of indices for all detected troubled cells.
"""
pass
def _apply_limiter(self, current_projection):
"""Applies limiter on troubled cells.
Parameters
----------
current_projection : ndarray
Matrix of projection of current update step for each polynomial
degree.
Returns
-------
new_projection : ndarray
Matrix of updated projection for each polynomial degree.
troubled_cells : list
List of indices for all detected troubled cells.
"""
troubled_cells = self._detector.get_cells(current_projection)
new_projection = self._limiter.apply(current_projection,
troubled_cells)
return new_projection, troubled_cells
class SSPRK3(UpdateScheme):
"""Class for strong stability-preserving Runge Kutta of order 3.
Notes
-----
Reference (?)
"""
# Override method of superclass
def _apply_stability_method(self, projection, cfl_number):
"""Applies stability method.
Parameters
----------
projection : ndarray
Matrix of projection for each polynomial degree.
cfl_number : float
CFL number to ensure stability.
Returns
-------
current_projection : ndarray
Matrix of projection of current update step for each polynomial
degree.
troubled_cells : list
List of indices for all detected troubled cells.
"""
original_projection = projection
current_projection = self._apply_first_step(original_projection,
cfl_number)
current_projection, __ = self._apply_limiter(current_projection)
current_projection = self._apply_second_step(original_projection,
current_projection,
cfl_number)
current_projection, __ = self._apply_limiter(current_projection)
current_projection = self._apply_third_step(original_projection,
current_projection,
cfl_number)
current_projection, troubled_cells = self._apply_limiter(
current_projection)
return current_projection, troubled_cells
def _apply_first_step(self, original_projection, cfl_number):
"""Applies first step of SSPRK3.
Parameters
----------
original_projection : ndarray
Matrix of original projection for each polynomial degree.
cfl_number : float
CFL number to ensure stability.
Returns
-------
ndarray
Matrix of updated projection for each polynomial degree.
"""
right_hand_side = self._equation.update_right_hand_side(
original_projection)
return original_projection + (cfl_number*right_hand_side)
def _apply_second_step(self, original_projection, current_projection,
cfl_number):
"""Applies second step of SSPRK3.
Parameters
----------
original_projection : ndarray
Matrix of original projection for each polynomial degree.
current_projection : ndarray
Matrix of projection of current update step for each polynomial
degree.
cfl_number : float
CFL number to ensure stability.
Returns
-------
ndarray
Matrix of updated projection for each polynomial degree.
"""
right_hand_side = self._equation.update_right_hand_side(
current_projection)
return 1/4 * (3*original_projection
+ (current_projection + cfl_number*right_hand_side))
def _apply_third_step(self, original_projection, current_projection,
cfl_number):
"""Applies third step of SSPRK3.
Parameter
---------
original_projection : ndarray
Matrix of original projection for each polynomial degree.
current_projection : ndarray
Matrix of projection of current update step for each polynomial
degree.
cfl_number : float
CFL number to ensure stability.
Returns
-------
ndarray
Matrix of updated projection for each polynomial degree.
"""
right_hand_side = self._equation.update_right_hand_side(
current_projection)
return 1/3 * (original_projection
+ 2*(current_projection + cfl_number*right_hand_side))