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TODO
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TODO
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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