Book in progress to illustrate Riemann solvers in Jupyter notebooks. @rjleveque, @ketch, and @maojrs.
We will start by collecting some things from the following repositories to work on: clawpack/riemann, clawpack/apps/notebooks, and clawpack/clawutil
##To do:
- Add dropdown to static interacts to select variable
- Phase space plots where you can drag q_l and q_r around
- Sliders for sample q_l and q_r inputs (in phase space, also in x-t plane?)
- Linked phase plane, q(x, t=1), and/or x-t plane plots as q_l, q_r change
##Problems
###One-dimensional
- Advection - conservative and color equation
- Acoustics - constant coefficient and arbitrary rho, K on each side
- Burgers' - with/without entropy fix
- Traffic flow - scalar and systems
- Buckley-Leverett
- Shallow water - Exact, Roe, HLLE (and with tracer)
- Shallow water with topography, Augmented solver
- p-system / nonlinear elasticity
- Euler - Exact, Roe, HLL, HLLE, HLLC,
- Euler with general EOS
- Reactive Euler
- HLL solver for arbitrary equations
- Layered shallow water
- MHD
- Relativistic Euler
- Dusty gas
- Two-phase flow
###Two-dimensional
- Elasticity
- Maxwell's equations
- Arbitrary normal direction on mapped grid
- Poro-elasticity (?)
- Description of the equations
- physical derivation
- Analysis of the hyperbolic structure:
- Jacobian; eigenvalues and eigenvectors
- Rankine-Hugoniot jump conditions
- Riemann invariants
- structure of centered rarefaction waves
- Riemann solvers
- Exact Riemann solver
- Approximate Riemann solvers
- Solvers for mapped grids
- Well-balanced solvers incorporating source terms
- Solvers with and without entropy fix
- Discussion and solvers for the transverse problem
- Comparisons
- Results using Clawpack with different solvers