This repository provides a numpy-based implementation of a one-sided higher order polynomial reconstruction algorithm based on so called central weighted essentially non-oscillatory (CWENO) reconstructions.

It is based on the work NAUMANN, Alexander; KOLB, Oliver; SEMPLICE, Matteo. On a third order CWENO boundary treatment with application to networks of hyperbolic conservation laws. Applied Mathematics and Computation, 2018, 325. Jg., S. 252-270. and takes the presented one dimensional 3rd order approach to higher orders of 5 and 7. It also provides two dimensional implementations by applying the one dimensional approach independently in each dimension.

Such reconstruction algorithms can for example be used to construct high-order Finite Volume schemes to solve systems of balance laws or conservation laws. Those arise from a variety of physical phenomena.

To assist with such applications, the repository implements explicit Runge-Kutta time integrators of order 3, 5, and 7 as well as methods to semi-discretize in spatial dimensions.

You can find a jupyter notebook show-casing the application to solve an initial value problem for shallow water equations in examples.

Contributions are always welcome. You can either pick an existing issue or create a new one.

In order to work on an issue just fork the repository and open a pull request once ready. Generally that means:

• all tests pass and
• if new functionality is added, corresponding tests are part of the pull request.

In order to run tests locally you can run

pip install -r requirements.txt -r test-requirements.txt
pip install -e .

from the source directory to first install all requirements and setup the repository in editable mode. If you prefer conda over pip use the equivalent commands to achieve the same.

If everything worked fine, you can run tests using pytest:

pytest tests/

I use ruff for code formatting. To automatically run ruff whenever you commit a change install the provided pre-commit hooks by running

pre-commit install

Afterwards you can also manually format the code executing for example

pre-commit run --all-files