numeric_ar_derivatives Subroutine

public subroutine numeric_ar_derivatives(eos, n, V, T, d_n, d_v, d_t, Ar, ArV, ArT, Arn, ArV2, ArT2, ArTV, ArVn, ArTn, Arn2)

numeric_ar_derivatives

Evaluate the Helmholtz derivatives with central finite difference.

Description

Tool to facilitate the development of new ArModel by testing the implementation of analytic derivatives.

Examples

 use yaeos, only: pr, SoaveRedlichKwong, ArModel
 use yaeos__consistency_armodel, only: numeric_ar_derivatives

 class(ArModel), allocatable :: model
 real(pr) :: tc(4), pc(4), w(4)

 real(pr) :: n(4), T, V

 real(pr) :: Ar_num, ArV_num, ArT_num, Arn_num(size(n)), ArV2_num, ArT2_num
 real(pr) :: ArTV_num, ArVn_num(size(n)), ArTn_num(size(n))
 real(pr) :: Arn2_num(size(n), size(n))

 n = [1.5, 0.2, 0.7, 2.3]
 tc = [190.564, 425.12, 300.11, 320.25]
 pc = [45.99, 37.96, 39.23, 40.21]
 w = [0.0115478, 0.200164, 0.3624, 0.298]

 T = 600_pr
 V = 0.5_pr

 model = SoaveRedlichKwong(tc, pc, w)

 call numeric_ar_derivatives(&
    model, n, V, T, d_n = 0.0001_pr, d_v = 0.0001_pr, d_t = 0.01_pr, &
    Ar=Ar_num, ArV=ArV_num, ArT=ArT_num, ArTV=ArTV_num, ArV2=ArV2_num, &
    ArT2=ArT2_num, Arn=Arn_num, ArVn=ArVn_num, ArTn=ArTn_num, &
    Arn2=Arn2_num &
    )

Arguments

Type IntentOptional Attributes Name
class(ArModel), intent(in) :: eos

Equation of state
real(kind=pr), intent(in) :: n(:)

Moles number vector
real(kind=pr), intent(in) :: V

Volume [L]
real(kind=pr), intent(in) :: T

Temperature [K]
real(kind=pr), intent(in) :: d_n

Moles finite difference step
real(kind=pr), intent(in) :: d_v

Volume finite difference step
real(kind=pr), intent(in) :: d_t

Temperature finite difference step
real(kind=pr), intent(out) :: Ar

Residual Helmoltz energy
real(kind=pr), intent(out), optional :: ArV

real(kind=pr), intent(out), optional :: ArT

real(kind=pr), intent(out), optional :: Arn(size(n))

real(kind=pr), intent(out), optional :: ArV2

real(kind=pr), intent(out), optional :: ArT2

real(kind=pr), intent(out), optional :: ArTV

real(kind=pr), intent(out), optional :: ArVn(size(n))

real(kind=pr), intent(out), optional :: ArTn(size(n))

real(kind=pr), intent(out), optional :: Arn2(size(n),size(n))


Variables

Type Visibility Attributes Name Initial
real(kind=pr), public :: Ar_aux1
real(kind=pr), public :: Ar_aux2
real(kind=pr), public :: Ar_aux3
real(kind=pr), public :: Ar_aux4
real(kind=pr), public :: dn_aux1(size(n))
real(kind=pr), public :: dn_aux2(size(n))
integer, public :: i
integer, public :: j