Book in progress to illustrate Riemann solvers in Jupyter notebooks. Contributors: @rjleveque, @ketch, and @maojrs.

Should the book start with some general chapters explaining important background? Or just jump into some simple hyperbolic systems and explain the concepts as they are encountered? Some of the things that need to be explained are:

• Similarity solutions
• Characteristics and characteristic velocities
• Conservation, weak solutions, and jump conditions
• Riemann invariants and integral curves
• How approximate solvers are used in numerical discretizations

Chapters with a complete draft have the box checked. Chapters that are required are in bold. The remaining chapters are optional and will depend on the authors finding time to complete them.

• Advection - conservative and color equation
• Acoustics - constant coefficient and arbitrary rho, K on each side - Mauricio
• Traffic flow - scalar - David
• Traffic flow with variable speed limit - David
• Burgers' - with/without entropy fix - Mauricio
• Buckley-Leverett - Randy
• Shallow water - Exact, Roe, HLLE (and with tracer) - Randy
• Shallow water with topography, Augmented solver - Randy
• p-system / nonlinear elasticity - David
• Euler - Exact, Roe, HLL, HLLE, HLLC
• Euler with general EOS - Mauricio
• Reactive Euler
• Traffic - systems
• LLF and HLL solvers for arbitrary equations
• Layered shallow water - David
• MHD
• Relativistic Euler
• Dusty gas
• Two-phase flow

• Elasticity - Mauricio
• Acoustics + mapped grids - Mauricio
• Shallow water
• Euler
• 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

• Acoustics, including transverse solver
• Elasticity, including transverse solver
• Shallow water equations

We are using bibtex for citations; add entries as necessary to riemann.bib. To insert a citation in a notebook, follow this pattern:

<cite data-cite="toro2013riemann"><a href="riemann.html#toro2013riemann">(Toro, 2013)<a></cite>

The value appearing in the html tag and the hyperlink should match the cite key in the bibtex file.

Use bibtex2html, downloadable from https://www.lri.fr/~filliatr/bibtex2html/. Then:

export TMPDIR=.
bibtex2html riemann.bib

This creates riemann.html which includes an anchor for each citation.

We are keeping the HTML file under version control for convenience, even though it is generated from the .bib file.

I've tested this with Jupyter 5.2.

jupyter nbconvert --to latex --template citations.tplx Euler_equations.ipynb
pdflatex Euler_equations
bibtex Euler_equations
pdflatex Euler_equations

This generates a single chapter with a bibliography at the end. To actually generate the book, we'll want to merge all the notebooks first; see discussion at jupyter/nbconvert#253.