KEYNOTE: Riemann problems for hyperbolic PDEs: Theory, software, and education

Time: 13:30 - 14:00   The Riemann problem is key to understanding the behavior of hyperbolic PDEs, and is the fundamental building block of many high-resolution shock-capturing numerical methods. The Riemann problem is... [ view full abstract ]

Time: 13:30 - 14:00  

The Riemann problem is key to understanding the behavior of hyperbolic PDEs, and is the fundamental building block of many high-resolution shock-capturing numerical methods. The Riemann problem is simply the PDE together with piecewise constant data, and the solution is typically a similarity solution consisting of waves propagating at constant speeds away from the discontinuity. I will briefly review this theory and the way these methods are used in the Clawpack software package (http://www.clawpack.org). I will then describe an ongoing project to write a book exploring true and approximate Riemann solutions for a wide variety of wave propagation problems. Jointly with David Ketcheson and Mauricio del Razo, we are developing the book as a series of Jupyter notebooks that include Python code for the reader to experiment with, and that employ interactive widgets and animation tools to provide a more active experience for students or researchers grappling with this theory. We are still experimenting with the best approach to developing material that works well in the notebook and also translates well to static webpages and hardcopy, with the hope of expanding its accessibility and usefulness. The current state of the project can be found in the Github repository https://github.com/clawpack/riemann_book.