2.3.16 Derivations of donor cell scheme
Donor cell scheme
(FTBS,
stencil in Sect. 2.3.11,
example later in Sect. 2.4.5):

(108) 

Discrete differences:
 Characteristic curves: mass flows from left to right
 Replacement: CS of naive scheme
difference in
upwind direction: BS

Characteristics + interpolation:
 Follow characteristic curve from back in time
 Interpolate between and (linearly)

ReconstructSolveAverage
(RSA, Godunovtype method):
 Finite volumes (reconstructionevolution, ReconstructPropagateAverage)
 Reconstruct run of within each cell (here: assume constant )
 Use exact continuous solution for the time evolution
 Average intermediate continuous result to get single value in each cell