.. _riemann:

Riemann problems and solutions
==============================

The links below might help explain Riemann problems and their solutions.


Acoustics
---------

 - The notebook `Riemann_problem_acoustics.ipynb
   <https://nbviewer.jupyter.org/url/depts.washington.edu/clawpack/v5.4.0alpha/_static/notebooks/Riemann_problem_acoustics.ipynb>`_
   illustrates the Riemann solution for the acoustics equations.

 - The webpage `phase plane <_static/phase_plane_acoustics.html>`_
   illustrates how the Riemann solution changes as the left
   state :math:`q_\ell` and right state :math:`q_r` are changed.  

Nonconvex Scalar conservation laws
----------------------------------

 - The notebook `Osher_Solution.ipynb
   <https://nbviewer.jupyter.org/url/faculty.washington.edu/rjl/classes/am574w2017/_static/Osher_Solution.ipynb>`_ 
   illustrates the Osher solution to scalar Riemann problems, 
   with nonconvex examples


Shallow water equations
-----------------------

 - The webpage `phase plane <_static/phase_plane_shallow_water_small.html>`_
   illustrates how the Riemann solution changes as the left
   state :math:`q_\ell` and right state :math:`q_r` are changed.