SWANS

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Authors: Thomas Bueler (1), Sam Delamere (2), Denys Dutykh (3), Alexei Rybkin (4), Alex Suleimani (5).

Affiliations: (1) Columbia University, (2) Bates College, (3) University of Savoie, (4) University of Alaska Fairbanks, (5) Arizona State University.

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Note: Users running versions of MATLAB previous to 2019a may encounter errors due to unsupported functions.

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### Introduction SWANS (Shallow Water Analytical Numerical Solver) provides a fast, direct comparison of a 1-D general finite volume solution to the 1+1 shallow water equations (SWE) with a 1-D analytical solution presented by Nicolsky et al (2018).

Installation

Users must download Chebfun. To do so, go to the Chebfun github repo (here). Follow the instructions in the Chebfun readme to install.

Note: If running this code through a command line interface, make sure chebfun is in your MATLAB path.

Download swe_runup from github here and note which directory the folder is saved to.

For users operating within MATLAB gui:

1. Navigate to swe_runup.
2. Open run_swe_runup and run script from editor.
3. Alternatively, if you are not running from the swe_runup folder, then you must add swe_runup to path from the gui. This can be done by right clicking on the folder and selecting Add to Path.

For users operating MATLAB from terminal window (macOS/linux):

1. Add MATLAB to your PATH.
2. Change directory path/to/swe_runup
3. matlab -nosplash -nodesktop
4. From the MATLAB CLI, type run_swe_runup

Usage

All simulations are produced through the run_swe_runup executable. All wave/simulation parameters are also located in this script. These include

• Simulation resolution (t_res and x_res)
• Plots (toggled 'on' or 'off')
• Order of data projection (n)
• Spatial and temporal domains (x0,Xf,t0,Tf)
• Beach slope (td)
• Initial wave function parameters (H1,H2,c2,c2,x1,x2).
• Initial wave functions (eta_0 and u_0)

Saving figures can be done through MATLAB's gui.

Third party packages.

Third party files included:

• genpath2: Adds all subfolders to path (excluding hidden files with .git extension).
• Hankel Transform: Computes fast/inverse fast Hankel transform.
• Chebfun

License

This package is free and open source. See LGPL-3.0 for more licensing information.

More information

A full account of software functionalities and implemented methods can be found here (link to paper).

Please file any comments or concerns through the github issue tracker here.

References

Nicolsky, Dmitry, et al. "General initial value problem for the nonlinear shallow water equations: Runup of long waves on sloping beaches and bays." Physics Letters A 382.38 (2018): 2738-2743.