drjod / yWaves

Solver for kinematic wave and Saint-Venant equations - Staggered scheme

yWaves

yWaves solves the 1D kinematic wave and Saint-Venant equations on a staggered grid by employing operator splitting (see e.g. http://www.tat.physik.uni-tuebingen.de/~kley/lehre/cp-prakt/projekte/projekt-kley.pdf). Implemented are the numerical schemes Upwind, Lax-Wendroff, Beam-Warming, Fromm as well as Leer- and Minmod-Slope limiter. The code was used in 2014 for the lecture hydrosystems analysis at Dresden Technical University, Germany. As far as I know, it is the first time that somebody uses the implemented numerical scheme in the context of surface runoff and flow networks. The following figure shows results of the dam break problem:

##Get yWaves run Requirements are Python and Matplotlib. Latter to get simulation results into plots, which are dynamically updated in runtime. I used the Anaconda Python distribution. This contains everything needed. The yWaves source code can be imported as

import sys
sys.path.append("path2yWaves")
import yWaves

To start a simulation, type then

yWaves.run("inputFile")

Make sure you set the paths correctly (you may need \\ instead \ on Windows). ##Input files A number of example input files are in the repository and cover various aspects of the code

1. damBreak.sim: The classic dam break (Riemann) problem. The analogy to the shock tube for the Euler equations;

2. runoff.sim: Precipitation runs off over an inclined plane;

3. shock.sim: A kinematic shock develops;

4. yJunction.sim: A (linear) advection wave forks at a junction;

5. infiltration.sim: An infiltration front percolates through two types of soil.

##Source code The main file yWaves.py generates a single instance of ySimulationClass that itself hosts an instance of yNetworkClass, yTimeSteppingClass, yNumericsClass, among others. Each instance of ySimulationClass hosts two instances of yBalanceClass and yGridClass. The grids alternate in their role as a primary grid and a partner grid, when mass and momentum (yBalanceClass) are calculated. Of course, in case of kinematic wave simulation the velocity update is based on constitutive relationships (yLawsClass). Implemented are the resistance to flow relationships by Manning and Darcy-Weissbach for runoff and Brooks-Corey for infiltration. They are assignes to yNetwork links (of yNodeClass) by their identity number. This way links can share a constitutive relationship or can have individual ones (see input file infiltration.sim).