Integrate field with LMM-SSP-VSS 3rd order class scheme.
Type | Intent | Optional | Attributes | Name | ||
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class(integrator_lmm_ssp_vss), | intent(inout) | :: | self | Integrator. |
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class(integrand_object), | intent(inout) | :: | U | Field to be integrated. |
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real(kind=R_P), | intent(in) | :: | Dt | Time step. |
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real(kind=R_P), | intent(in) | :: | t | Time. |
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subroutine integrate_order_3(self, U, Dt, t)
!< Integrate field with LMM-SSP-VSS 3rd order class scheme.
class(integrator_lmm_ssp_vss), intent(inout) :: self !< Integrator.
class(integrand_object), intent(inout) :: U !< Field to be integrated.
real(R_P), intent(in) :: Dt !< Time step.
real(R_P), intent(in) :: t !< Time.
real(R_P) :: omega_ !< Omega coefficient.
omega_= omega(Dt=self%Dt, s=self%steps-1)
U = (self%previous(1) * ((3._R_P * omega_ + 2._R_P) / omega_ ** 3 )) + &
(self%previous(self%steps) * (((omega_ + 1._R_P) ** 2) * (omega_ - 2._R_P) / omega_ ** 3)) + &
(self%previous(1)%t(t=self%t(1)) * (self%Dt(self%steps) * (omega_ + 1._R_P) / omega_ ** 2)) + &
(self%previous(self%steps)%t(t=self%t(self%steps)) * (self%Dt(self%steps) * (omega_ + 1._R_P) ** 2 / omega_ ** 2))
if (self%autoupdate) call self%update_previous(U=U, previous=self%previous, Dt=Dt, t=t, previous_Dt=self%Dt, previous_t=self%t)
endsubroutine integrate_order_3