| | 14 | |
| | 15 | == The method == |
| | 16 | |
| | 17 | In conservative form, the Godunov method is written: |
| | 18 | |
| | 19 | u(i, n+1) = u(i, n) + delta_t/delta_x*[F(i-1/2) - F(i+1/2)] |
| | 20 | |
| | 21 | where F(i-1/2) is the numerical flux, which = F(u(i+1/2, 0)) (i.e. the physical flux evaluated using the solution to local RP) |
| | 22 | |
| | 23 | where delta_t is constrained by the delta_t <= delta_x/max[S(n)] <- note this allows a wave to travel a full delta_x in a time-step |
| | 24 | |
| | 25 | we don't worry about wave-wave interaction based on linearity -- that is, assume wave interactions do not lead to wave accelerations |
| | 26 | |
| | 27 | u(i, n+1) = average over the cell |
