bdf_time_scheme.f90

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module bdf_time_scheme
  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) :: bdf_time_scheme_t
   contains
     procedure, nopass :: compute_coeffs => bdf_time_scheme_compute_coeffs
  end type bdf_time_scheme_t
 
contains
 
  subroutine bdf_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
 
    call rzero(coeffs, 4)
 
    ! Note, these are true coeffs, multiplied by dt(1)
    select case (order)
    case (1)
       coeffs(1) = 1.0_rp
       coeffs(2) = 1.0_rp
    case (2)
       coeffs(1) = (1 + dt(1)/(dt(1) + dt(2)))
       coeffs(3) = -dt(1)**2/dt(2)/(dt(1) + dt(2))
       coeffs(2) = coeffs(1) - coeffs(3)
    case (3)
       coeffs(2) = (dt(1) + dt(2)) * (dt(1) + dt(2) + dt(3)) / &
            (dt(1) * dt(2) * (dt(2) + dt(3)))
       coeffs(3) = -dt(1) * (dt(1) + dt(2) + dt(3)) / &
            (dt(2) * dt(3) * (dt(1) + dt(2)))
       coeffs(4) = dt(1) * (dt(1) + dt(2)) / &
            (dt(3) * (dt(2) + dt(3)) * (dt(1) + dt(2) + dt(3)))
       coeffs(1) = coeffs(2) + coeffs(3) + coeffs(4)
       coeffs = coeffs * dt(1)
    case default
       call neko_error("The order of the BDF time scheme must be 1 to 3.")
    end select
 
  end subroutine bdf_time_scheme_compute_coeffs
 
end module bdf_time_scheme