ab_time_scheme.f90

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module ab_time_scheme
  use neko_config
  use num_types, only : rp
  use time_scheme, only: time_scheme_t
  use math, only : rzero
  use utils, only : neko_error
  implicit none
  private
 
  type, public, extends(time_scheme_t) :: ab_time_scheme_t
   contains
     procedure, nopass :: compute_coeffs => ab_time_scheme_compute_coeffs
  end type ab_time_scheme_t
 
contains
 
  subroutine ab_time_scheme_compute_coeffs(coeffs, dt, order)
    implicit none
    real(kind=rp), intent(out) :: coeffs(4)
    real(kind=rp), intent(in) :: dt(10)
    integer, intent(in) :: order
    real(kind=rp) dta, dtb, dtc, dtd, dte, dts
 
    call rzero(coeffs, 4)
 
    select case (order)
    case (1)
       coeffs(1) = 1.0_rp
    case (2)
       coeffs(2) = -0.5_rp * dt(1) / dt(2)
       coeffs(1) =  1.0_rp - coeffs(2)
    case (3)
       dts =  dt(2) + dt(3)
       dta =  dt(1) / dt(2)
       dtb =  dt(2) / dt(3)
       dtc =  dt(1) / dt(3)
       dtd =  dts / dt(2)
       dte =  dt(1) / dts
       coeffs(3) =  dte*( 0.5_rp*dtb + dtc/3.0_rp )
       coeffs(2) = -0.5_rp * dta - coeffs(3) * dtd
       coeffs(1) =  1.0_rp - coeffs(2) - coeffs(3)
    case default
       call neko_error("The order of the AB time scheme must be 1 to 3.")
    end select
 
  end subroutine ab_time_scheme_compute_coeffs
 
end module ab_time_scheme