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An interactive book about the Riemann problem for hyperbolic PDEs, using Jupyter notebooks. Work in progress.

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Riemann Problems and Jupyter Solutions

by David I. Ketcheson, Randall J. LeVeque, and Mauricio del Razo Sarmina

This repository contains source files for a book that illustrates Riemann solutions and approximate Riemann solvers in Jupyter notebooks. The print version of the book is available from SIAM, and also as an ebook. You can view a pdf version of the contents, preface, and index.

Riemann Problems and Jupyter Solutions
    Theory and Approximate Solvers for Hyperbolic PDEs
by David I. Ketcheson, Randall J. LeVeque, and Mauricio J. del Razo
SIAM, 2020.   ISBN: 978-1-611976-20-5
ebook: DOI 10.1137/1.9781611976212

See for additional information and links to the html rendered notebooks. These are static views (no execution or interactive widgets), but some notebooks include animations that will play.

The recommended way to fully experience the book is by running the Jupyter notebooks:

Start from the table of contents given in the notebook Index.ipynb, which is also shown below. The notebook Index2.ipynb lists some notebooks that are not in the SIAM book, some of which are still under development. Additional notebooks may appear in the future.


The FA16 branch of this repository corresponds to notebooks as converted into the SIAM book. The master branch may be updated in the future.


To install the dependencies, first install a Fortran compiler. Then do the following in a terminal:

pip install clawpack
git clone
cd riemann_book
pip install -r requirements.txt
jupyter nbextension enable --py widgetsnbextension
pip install jupyter_contrib_nbextensions
jupyter contrib nbextension install --user
jupyter nbextension enable equation-numbering/main

You can test your installation by running


A table of contents and suggested order for reading the notebooks is given in Index.ipynb.

If you want to compile the PDF locally, you must also install the package bookbook.


Rather than installing all the dependencies, if you have Docker installed you can use

$ docker pull clawpack/rbook

to obtain a docker image that has all the notebooks and dependencies installed. This was built using the Dockerfile in this repository, which could be modified to build a new image also containing other material, if desired. See for further instructions.

Execute in the cloud


Rather than installing anything on your own computer, you can run the notebooks on the cloud using the free binder service.
Simply navigate to this link in a browser:

This may take a few minutes to start up a notebook server on a Jupyterhub. Then navigate to

and open
to get started.



The code in this repository, including all code samples in the notebooks, is released under the 3-Clause BSD License. See LICENSE-CODE for the license and read more at the Open Source Initiative.


The text content of the notebooks is released under the CC-BY-NC-ND License. See for the license and read more at Creative Commons.


Taken from the notebook Index.ipynb, these are the notebooks that also appear in the printed book:

  • Preface -- Describes the aims and goals, and different ways to use the notebooks.
  • Part I: The Riemann problem and its solution
    • Introduction.ipynb
      -- Introduces basic ideas with some sample solutions.
    • Advection.ipynb
      -- The scalar advection equation is the simplest hyperbolic problem.
    • Acoustics.ipynb
      -- This linear system of two equations illustrates how eigenstructure is used.
    • Burgers.ipynb
      -- The classic nonlinear scalar problem with a convex flux.
    • Traffic_flow.ipynb
      -- A nonlinear scalar problem with a nice physical interpretation.
    • Nonconvex_scalar.ipynb
      -- More interesting Riemann solutions arise when the flux is not convex.
    • Shallow_water.ipynb
      -- A classic nonlinear system of two equations.
    • Shallow_tracer.ipynb
      -- Adding a passively advected tracer and a linearly degenerate field.
    • Euler.ipynb
      -- The classic equations for an ideal gas.
  • Part II: Approximate solvers
    • Approximate_solvers.ipynb
      -- Introduction to two basic types of approximations.
    • Burgers_approximate.ipynb
      -- Approximate solvers for a scalar problem.
    • Shallow_water_approximate.ipynb
      -- Roe solvers, the entropy fix, positivity, HLL, and HLLE.
    • Euler_approximate.ipynb
      -- Extension of these solvers to gas dynamics.
    • FV_compare.ipynb
      -- Comparing how different approximate solvers perform when used with PyClaw.

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