boundaryscheme 2.4

This library implements Kreiss-Lopatinskii determinant for numerical scheme with boundary

This is the architecture for the package "boundaryscheme" : https://pypi.org/project/boundaryscheme/

boundaryscheme

Package Python to use numerical scheme with boundaries which is described in the PhD manuscript

P. Le Barbenchon, Étude théorique et numérique de la stabilité GKS pour des schémas d'ordre élevé en présence de bords, PhD, 2023.

Package documentation

https://plebarbenchon.github.io/boundaryscheme

Easy installation for the PyPI version

pip install boundaryscheme

Installation for the GitHub version

git clone https://github.com/PLeBarbenchon/boundaryscheme.git
cd boundaryscheme
pip3 install -r requirements.txt
pip3 install -e .
python3 examples/draw_detKLcurve.py

Example

import matplotlib.pyplot as plt

from boundaryscheme.schemes import BeamWarming
from boundaryscheme.boundaries import SILW
import boundaryscheme.pyplot as bsplt

bsplt.detKLcurve(BeamWarming, SILW(2,3),lambdacursor = True)
plt.show()

Creation of a scheme

To compute the scheme $U_{j}^{n+1} = \dfrac{1}{3}U_{j-1}^n + U_j^n -\dfrac{1}{6} U_{j+1}^n - \dfrac{1}{6}U_{j+2}^n$ with a boundary $B$, write

S = Scheme([1/3,1,-1/6,-1/6],1, B) 

To compute the scheme depending on a parameter $\lambda$, create a Python class using the following formulation:

class Name(Scheme):
    """This is a class to represent ...

    :param lamb: The Courant number, i.e  a.dt/dx where "a" is the velocity, "dt" the time discretization and "dx" the space discretization
    :type lamb: float
    :param boundary: Boundary condition, defaults to Dirichlet()
    :type boundary: class:`Boundary`, optional
    :param sigma: Gap between the mesh and the boundary condition, defaults to 0
    :type sigma: float, optional
    """

    def __init__(self, lamb, boundary=Dirichlet(), sigma=0, **kwargs):
        """Constructor method"""
        self.sigma = sigma
        self.lamb = lamb
        self.inter = #write the list of the coefficients of the scheme
        self.center = #write the index of the center of the scheme
        self.CFL = #give the CFL condition
        super().__init__(inter=self.inter, center=self.center, boundary=boundary, sigma=sigma, **kwargs)

    def shortname(self):
        """Name method"""
        return "Name"

For example, to compute the scheme $U_{j}^{n+1} = \dfrac{\lambda}{3}U_{j-1}^n + \lambda^2 U_j^n -\dfrac{1}{6} U_{j+1}^n - \dfrac{\lambda}{6}U_{j+2}^n$ with a boundary $B$, write

class Name(Scheme):
    def __init__(self, lamb, boundary=Dirichlet(), sigma=0, **kwargs):
        self.sigma = sigma
        self.lamb = lamb
        self.inter = [lamb/3, lamb**2, -1/6, -lamb/6]
        self.center = 1
        self.CFL = #give the CFL condition
        super().__init__(inter=self.inter, center=self.center, boundary=boundary, sigma=sigma, **kwargs)

    def shortname(self):
        """Name method"""
        return "Name"

Citing

The code is citable via Zenodo. Please cite as:

P. Le Barbenchon, boundaryscheme: package Python for numerical schemes with boundaries. 2023.