https://github.com/joshualampert/2024_dispersive_shallow_water
Reproducibility repository for the paper "Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations"
https://github.com/joshualampert/2024_dispersive_shallow_water
Last synced: 3 months ago
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Reproducibility repository for the paper "Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations"
- Host: GitHub
- URL: https://github.com/joshualampert/2024_dispersive_shallow_water
- Owner: JoshuaLampert
- License: mit
- Created: 2024-02-26T14:41:34.000Z (over 1 year ago)
- Default Branch: main
- Last Pushed: 2025-02-20T19:19:13.000Z (4 months ago)
- Last Synced: 2025-02-20T20:26:57.634Z (4 months ago)
- Language: Julia
- Homepage:
- Size: 196 KB
- Stars: 1
- Watchers: 3
- Forks: 2
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations
[](https://opensource.org/licenses/MIT)
[](https://doi.org/10.5281/zenodo.10709026)
This repository contains information and code to reproduce the results presented in the
article
```bibtex
@online{lampert2024structure,
title={Structure-Preserving Numerical Methods for Two Nonlinear Systems of
Dispersive Wave Equations},
author={Lampert, Joshua and Ranocha, Hendrik},
year={2024},
month={02},
eprint={2402.16669},
eprinttype={arxiv},
eprintclass={math.NA}
}
```
If you find these results useful, please cite the article mentioned above. If you
use the implementations provided here, please **also** cite this repository as
```bibtex
@misc{lampert2024structureRepro,
title={Reproducibility repository for
"{S}tructure-Preserving Numerical Methods
for Two Nonlinear Systems of Dispersive Wave Equations"},
author={Lampert, Joshua and Ranocha, Hendrik},
year={2024},
howpublished={\url{https://github.com/JoshuaLampert/2024\_dispersive\_shallow\_water}},
doi={10.5281/zenodo.10709026}
}
```
and [DispersiveShallowWater.jl](https://github.com/JoshuaLampert/DispersiveShallowWater.jl) as
```bibtex
@misc{lampert2023dispersive,
title={{D}ispersive{S}hallow{W}ater.jl: {S}tructure-preserving numerical
methods for dispersive shallow water models},
author={Lampert, Joshua},
year={2023},
month={10},
howpublished={\url{https://github.com/JoshuaLampert/DispersiveShallowWater.jl}},
doi={10.5281/zenodo.10034636}
}
```
## Abstract
We use the general framework of summation-by-parts operators
to construct conservative, energy-stable and well-balanced
semidiscretizations of two different nonlinear systems of
dispersive shallow water equations with varying bathymetry:
(i) a variant of the coupled Benjamin-Bona-Mahony (BBM) equations
and (ii) a recently proposed model by Svärd and Kalisch (2025) with
enhanced dispersive behavior. Both models share the property of
being conservative in terms of a nonlinear invariant, often
interpreted as energy. This property is preserved exactly
in our novel semidiscretizations. To obtain fully-discrete
energy-stable schemes, we employ the relaxation method.
Our novel methods generalize energy-conserving
methods for the BBM-BBM system to variable bathymetries. Compared to the
low-order, energy-dissipative finite volume method proposed by Svärd and Kalisch,
our schemes are arbitrary high-order accurate, energy-conservative or -stable,
can deal with periodic and reflecting boundary conditions, and can be any
method within the framework of summation-by-parts operators including
finite difference and finite element schemes.
We present improved numerical properties of our methods in some test cases.
## Numerical experiments
To reproduce the numerical experiments presented in this article, you need
to install [Julia](https://julialang.org/). The numerical experiments presented
in this article were performed using Julia v1.11.2.
First, you need to download this repository, e.g., by cloning it with `git`
or by downloading an archive via the GitHub interface. Then, you need to start
Julia in the `code` directory of this repository and follow the instructions
described in the `README.md` file therein.
## Authors
- Joshua Lampert (University of Hamburg, Germany)
- [Hendrik Ranocha](https://ranocha.de) (Johannes Gutenberg University Mainz, Germany)
## License
The code in this repository is published under the MIT license, see the
`LICENSE` file.
## Disclaimer
Everything is provided as is and without warranty. Use at your own risk!