Here, 10 different numerical solvers for the right hand sides of the biogeochemical models are implemented for computing the ordinary differential equations (ODEs) which are calculated as the second step of the operational split method for the complete biogeochemical models. The remaining ODE is
These methods are:
The schemes 1 - 5 and 7 - 8 have been described in detail by Burchard et al. (2003). Later, Bruggeman et al. (2006) could show that the Modified Patankar schemes 7 - 8 are only conservative for one limiting nutrient and therefore they developed the Extended Modified Patankar (EMP) schemes 10 and 11 which are also stoichiometrically conservative. Patankar and Modified Patankar schemes of fourth order have not yet been developed, such that choices 6 and 9 do not work yet.
The call to ode_solver() requires a little explanation. The first argument solver is an integer and specifies which solver to use. The arguments numc and nlev gives the dimensions of the data structure cc i.e. cc(1:numc,0:nlev). dt is simply the time step. The last argument is the most complicated. right_hand_side is a subroutine with a fixed argument list. The subroutine evaluates the right hand side of the ODE and may be called more than once during one time-step - for higher order schemes. For an example of a correct right_hand_side have a look at e.g. do_bio_npzd()
IMPLICIT NONEINPUT PARAMETERS:
integer, intent(in) :: solver,nlev,numc REALTYPE, intent(in) :: dt !INPUT/OUTPUT PARAMETER: REALTYPE, intent(inout) :: cc(1:numc,0:nlev) interface subroutine right_hand_side_ppdd(first,numc,nlev,cc,pp,dd) logical, intent(in) :: first integer, intent(in) :: numc,nlev REALTYPE, intent(in) :: cc(1:numc,0:nlev) REALTYPE, intent(out) :: pp(1:numc,1:numc,0:nlev) REALTYPE, intent(out) :: dd(1:numc,1:numc,0:nlev) end end interface interface subroutine right_hand_side_rhs(first,numc,nlev,cc,rhs) logical, intent(in) :: first integer, intent(in) :: numc,nlev REALTYPE, intent(in) :: cc(1:numc,0:nlev) REALTYPE, intent(out) :: rhs(1:numc,0:nlev) end end interfaceREVISION HISTORY:
Original author(s): Hans Burchard, Karsten BoldingLOCAL VARIABLES:
Karsten Bolding 2012-01-24