Suggestions for Working Through Toro

  • Read Chs 1-3 on the Euler equations and solutions to hyperbolic equations in general. Some of this will likely be familiar.
  • Read Ch 4 and write the exact Euler solver described.
  • Read Ch 5 and write the Godunov upwind scheme, for the linear systems described.
  • Read Ch 6 and update the Godunov upwind scheme to use the exact Euler solver.
  • Skip 7&8
  • Read Ch 9 and write the approximate-state solvers (good place to find out if you're following good programming practices).
  • Read/skim Chs 10-12 and write at least the HLLC solver (which is the one used in AstroBEAR). Note that there have been some significant improvements to the HLLC chapter in the third edition. Write the rest if you're interested, though I wouldn't recommend the Osher solver (it's interesting mathematically, but doesn't seem to offer much over the other solvers).
  • Read Ch 16 and write a 2D/3D solver (test problem in Ch 17). Another place where you'll really notice if you've been following good practice.
  • For second-order solvers: Read Ch 14 (skim 13 for an introduction to the same concepts for scalar equations) and write the WAF and MUSCL schemes (esp. MUSCL-Hancock, used in AstroBEAR).

Note that the ends of the code-related chapters have example code. I'd strongly suggest looking at some modern Fortran style guides rather than following the old style given in these, not least because it's much easier to follow your own code if it's written with meaning.

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