TODO

Add implementation details throughout, explaining how to translate stuff into code
   -- maybe in the margins with the Tufte class?

https://en.wikipedia.org/wiki/Shallow_water_equations#/media/File:Characteristics_saint-venant.svg

new chapters:

  -- self-gravity

  -- radiation hydro

  -- AMR

  -- mapped grids

     * general quadralateral grids

     * moving grids

       - 1-d moving grid showing 
     
  -- MHD

  -- relativisitc

  -- WENO

  -- higher-order

     o method of lines integration with RK3/4 and high-order reconstruction

  -- implicit hydro

  -- shallow water

  -- cosmological flows

  -- understanding simulations

     * convergence tests

     * sanity checks

     * parameter studies vs. hero calculations

  -- volume of fluid




sample of public codes

  -- Athena
  -- Castro
  -- Enzo
  -- Flash
  -- Maestro
  -- Pluto
  -- Zeus


=======================

Chapter 2:

 -- in "what is a simulation", add a discussion of DNS, LES, and ILES

 -- add BC and difference on a grid examples perhaps through a ipython
    notebook.



=======================

Chapter 4:

 -- add a notebook showing FTCS and upwind on a simple FV grid
 
 pyro exercises:

 -- try out different limiters


=======================

Chapter 5:


 -- exercise: notebook showing burgers' solution


=======================

Chapter 6/7:

 -- add a figure for section 5.2.1, showing piecewise constant
    reconstruction

 -- add a discussion (interlude) motivating how limiters are derived

 -- bulletted list on different Riemann solvers

 -- derive the jump conditions and the entropy conditions for the 
    Riemann problem and show the function we zero.

 -- implementation detail: for Riemann solvers, usually the godunov
    velocity is set to 0 at symmetry boundaries

 -- it is important to odd-reflect the gravitational acceleration 
    at reflecting boundaries

 examples:

   -- 1-d Riemann solver
   -- 1-d Godunov

 pyro...


=======================

Multigrid chapter:

 examples:

   -- 1-d relaxation
   -- 1-d MG


=======================

Diffusion chapter:


  examples:
    
    -- 1-d diffusion solver
    
  pyro


----

reference for the choice of epsilon in numerical derivatives as
\sqrt{machine epsilon} -- this gives some suggestions:
http://mathoverflow.net/questions/28463/optimum-small-number-for-numerical-differentiation


----

tcolorbox for exercises:

http://tex.stackexchange.com/questions/172475/how-can-i-define-a-custom-tcolorbox-environment-with-color-as-a-parameter


http://www.scriptscoop2.com/t/e6de0140d668/counters-for-chapter-and-section-environments-when-using-tcolorbox-for.html


http://tex.stackexchange.com/questions/254401/use-the-exercise-environment-from-legrand-book-template

http://www.latextemplates.com/template/the-legrand-orange-book