Second-order Runge-Kutta scheme

INTERFACE:

    subroutine runge_kutta_2(dt,numc,nlev,cc,right_hand_side)

DESCRIPTION:

Here, the second-order Runge-Kutta (RK2) scheme is coded, with two evaluations of the right hand side per time step:

$$\left. \begin{array}{rcl} c_i^{(1)} &=& \displaystyle c_i^n + \De... ...}^n\right) - D_i\left(\underline{c}^{(1)}\right) \right\}. \end{array} \right\}$$ (249)

USES:

    IMPLICIT NONE

INPUT PARAMETERS:

    REALTYPE, intent(in)                :: dt
    integer, intent(in)                 :: numc,nlev
   !INPUT/OUTPUT PARAMETER:
    REALTYPE, intent(inout)             :: cc(1:numc,0:nlev)
 
    interface
       subroutine right_hand_side(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 interface

REVISION HISTORY:

    Original author(s): Hans Burchard, Karsten Bolding

LOCAL VARIABLES:

   logical  :: first
   REALTYPE :: rhs(1:numc,0:nlev),rhs1(1:numc,0:nlev)
   REALTYPE :: cc1(1:numc,0:nlev)
   integer  :: i,ci