Coupling with external sources (soot, spray, radiation, etc) could be made tighter by recomputing the external forcing at step/iteration (n+1,k) during the SDC iteration process, and using S_{n+1/2} = 0.5(S_n + S_{n+1}) as the effective forcing. #427 moves in this direction but doe not fully implement that yet.
If the present implementation is left alone, Div u should be recomputed at the beginning of each timestep, such that it is using the external forcing for the new timestep rather than the old timestep. A consequence of not recomputing Div u is that spray sources are not included at all for the first timestep when computing Div u in the current implementation.