# Riemann problems and solutions¶

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

## Acoustics¶

• The notebook Riemann_problem_acoustics.ipynb illustrates the Riemann solution for the acoustics equations.
• The webpage phase plane illustrates how the Riemann solution changes as the left state $$q_\ell$$ and right state $$q_r$$ are changed.

## Nonconvex Scalar conservation laws¶

• The notebook Osher_Solution.ipynb illustrates the Osher solution to scalar Riemann problems, with nonconvex examples

## Shallow water equations¶

• The webpage phase plane illustrates how the Riemann solution changes as the left state $$q_\ell$$ and right state $$q_r$$ are changed.