Metadata-Version: 2.1
Name: SWE_Solver
Version: 0.0.6
Summary: A small package including a one-dimensional well-balanced Shallow Water Equations solver.
Author-email: Daniel Cortild <d.cortild@rug.nl>
Project-URL: Homepage, https://github.com/DanielCortild/SWE-Solver
Project-URL: Bug Tracker, https://github.com/DanielCortild/SWE-Solver/issues
Classifier: Programming Language :: Python :: 3
Classifier: License :: OSI Approved :: MIT License
Classifier: Operating System :: OS Independent
Requires-Python: >=3.7
Description-Content-Type: text/markdown
License-File: LICENSE

# Shallow Water Equations Solver

This package provides a well-balanced solver for the one-dimensional Saint-Venant equations, based on the principles outlined in [this paper](XXX).

## Usage

To utilize this package, you can call the `plotSWE` function with the following parameters:

```
h, u = plotSWE(B, h0, u0, Nx, tEnd, timePoints, g=1, method='C')
```
### Parameters:
* **B** _(callable)_: Bottom topography function. This function defines the topographic profile and should take spatial coordinates as input and return the bottom elevation at those coordinates. In case of `method='A'`, should be an array of two callables, representing B and its derivative.
* **h0** _(array)_: Initial water height profile. This should be an array of length `Nx`, representing the initial water height at different spatial locations.
* **u0** _(array)_: Initial water velocity profile. Similar to h0, this should be an array of length `Nx`, representing the initial water velocity at different spatial locations.
* **Nx** _(int)_: Number of spatial grid points.
* **tEnd** _(float)_: End time of the simulation. The simulation starts at time t=0.
* **timePoints** _(list)_: List of time points at which you want to visualize the results.
* **g** _(float, optional)_: Gravitational constant. Default is `1`.
* **method** _(str, optional)_: Method selection (`'A'`, `'B'` or `'C'`). Default is `'C'`.

### Returns:
* **h** _(array)_: Array containing the water height profile at the final time point.
* **u** _(array)_: Array containing the water velocity profile at the final time point.

## Example:

```
from SWE_Solver import plotSWE
from math import sqrt
from scipy.special import erf

Nx = 100
B = lambda x: 1
f = lambda T: 1 + sqrt(3) / (1 - erf(-0.5 / 0.1)) * (erf((T - 0.5) / 0.1) - erf (-0.5 / 0.1))
h0 = [f(_/ (Nx-1)) for _ in range(Nx)]
u0 = [2.0 / h0[_] for _ in range(Nx)]
_ = plotSWE(B, h0, u0, Nx, tEnd=1.0, timePoints=[0.0, 0.1, 0.5, 1.0])
```

In this example, we're using a spatial grid with 100 points, running the simulation up to `t=1` seconds, and visualizing the results at times `0.0`, `0.1`, `0.5` and `1.0` seconds, with gravitational constant `g=1` (default value) and using `method='C'` (default value).

This produces the result in the following figure.

![](https://github.com/DanielCortild/SWE-Solver/blob/main/fig.png?raw=true)
