2.6.1 Godunov's idea
Discretization paradigms (see Sect. 2.3.16):
- Finite differences: replace derivatives by differences
- Characteristics: follow characteristics back in time and interpolate at old time-level
- Reconstruct-Solve-Average (RSA): Godunov-type finite-volume scheme
Note: Exact solution (and reconstruction) can handle shocks
numerical scheme can handle shocks.
Solve the exact problem for : shift reconstructed function.
in each cell
to get .