public function F_critical(model, X, ns, S, z0, zi, u)

F_critical

Description

Function that should be equal to zero at a critical point is found. The second criticality condition is calculated as a numerical derivative with eps=1e-10.

$$F = \begin{bmatrix} \lambda_1(s) \\ \frac{\partial \lambda_1(s+\epsilon) - \lambda_1(s-\epsilon)}{2\epsilon} \\ \ln P - X_4 \\ X_{ns} - S \end{bmatrix} = 0$$

Arguments

Type	Intent	Optional	Attributes		Name
class(ArModel),	intent(in)			::	model	Equation of state model
real(kind=pr),	intent(in)			::	X(4)	Vector of variables
integer,	intent(in)			::	ns	Position of the specification variable
real(kind=pr),	intent(in)			::	S	Specification variable value
real(kind=pr),	intent(in)			::	z0(:)	Molar fractions of the first fluid
real(kind=pr),	intent(in)			::	zi(:)	Molar fractions of the second fluid
real(kind=pr),	intent(in)			::	u(:)	Eigen-vector

Return Value real(kind=pr), (4)

Variables

Type	Visibility	Attributes		Name		Initial
real(kind=pr),	public		::	P
real(kind=pr),	public		::	T
real(kind=pr),	public		::	V
real(kind=pr),	public,	parameter	::	eps	=	1e-5_pr
real(kind=pr),	public		::	z(size(u))