Evans solvers and time-evolution solvers for 2d inclined inviscid Saint-Venant equations

Multidimensional Stability and Transverse Bifurcation of Hydraulic Shocks and Roll Waves in Open Channel Flow

Matlab codes for Evans function solvers and Python codes for numerical time evolutions of 2d- hydraulic shocks and roll waves of inviscid Saint-Venant equations 

Authors: Zhao Yang and Kevin Zumbrun 

For questions/comments please contact either the first author via yangzhao@amss.ac.cn or the second author via kzumbrun@indiana.edu

Prerequisites

Programs

• Python 
• Matlab 

Python libraries

• Clawpack

           Clawpack Development Team (2022), Clawpack Version 5.9.0, http://www.clawpack.org, doi: 10.5281/zenodo.7026045

  
Description 

Evans solvers

Inside the folder Evans solvers and its subfolders, one can find codes for Evans/Evans-Lopatinsky solvers for smooth hydraulic shocks and discontinuous hydraulic shocks and a periodic Evans-Lopatinsky solver for roll waves, respectively.

time-evolution solvers

Inside the folder time-evolution solvers and its subfolders, one can find sample python codes for generating time-evolution raw data files for the 2d inviscid Saint-Venant equations with either dam-break or roll waves initial data. One can also find matlab codes that make use of the raw data files to create movies.

Movies are downloadable from https://doi.org/10.5281/zenodo.8199967.

data

Inside the folder data, one can find boundaries.mat which contains raw datum of various stability boundaries of the 2d inviscid roll waves.