Detailed Description

Definition at line 108 of file GeneralizedCubic.h.

#include <GeneralizedCubic.h>

Inheritance diagram for AbstractCubic:

Public Member Functions
	AbstractCubic (const std::vector< double > &Tc, std::vector< double > pc, std::vector< double > acentric, double R_u, double Delta_1, double Delta_2, const std::vector< double > &C1=std::vector< double >(), const std::vector< double > &C2=std::vector< double >(), const std::vector< double > &C3=std::vector< double >())
	The abstract base clase for the concrete implementations of the cubic equations of state. More...

virtual	~AbstractCubic ()=default

void	set_alpha (const std::vector< double > &C1, const std::vector< double > &C2, const std::vector< double > &C3)
	Set the constants for the Mathias-Copeman alpha function, or if C1,C2,C3 are all empty, set the default alpha model. More...

void	set_alpha_function (std::size_t i, shared_ptr< AbstractCubicAlphaFunction > &acaf)
	Set the alpha function for the i-th component. More...

shared_ptr< AbstractCubicAlphaFunction >	get_alpha_function (std::size_t i)
	Get the alpha function for the i-th component. More...

const std::vector< shared_ptr< AbstractCubicAlphaFunction > > &	get_all_alpha_functions ()
	Get all the alpha functions. More...

void	set_all_alpha_functions (const std::vector< shared_ptr< AbstractCubicAlphaFunction > > &alpha)
	Set all the alpha functions. More...

const std::vector< std::vector< double > > &	get_kmat ()
	Get the entire kij matrix in one shot. More...

void	set_kmat (const std::vector< std::vector< double > > &k)
	Set the entire kij matrix in one shot. More...

void	set_kij (std::size_t i, std::size_t j, double val)
	Set the kij factor for the ij pair. More...

double	get_kij (std::size_t i, std::size_t j)
	Get the kij factor for the ij pair. More...

std::vector< double > &	get_Tc ()
	Get the vector of critical temperatures (in K) More...

std::vector< double > &	get_pc ()
	Get the vector of critical pressures (in Pa) More...

std::vector< double > &	get_acentric ()
	Get the vector of acentric factors. More...

double	get_Delta_1 ()
	Read-only accessor for value of Delta_1. More...

double	get_Delta_2 ()
	Read-only accessor for value of Delta_2. More...

double	get_R_u ()
	Read-only accessor for value of R_u (universal gas constant) More...

void	set_Tr (double Tr)
	Set the reducing temperature to be used. More...

void	set_rhor (double rhor)
	Set the reducing density to be used. More...

double	get_Tr ()
	Get the reducing temperature to be used. More...

double	get_rhor ()
	Get the reducing density to be used. More...

void	set_C_MC (std::size_t i, double c1, double c2, double c3)
	Set the three Mathias-Copeman constants in one shot for the component i of a mixture. More...

void	set_C_Twu (std::size_t i, double L, double M, double N)
	Set the three Twu constants in one shot for the component i of a mixture. More...

virtual double	a0_ii (std::size_t i)=0

virtual double	b0_ii (std::size_t i)=0

virtual double	m_ii (std::size_t i)=0
	Get the m_ii variable in the alpha term inculuded in the attractive part. More...

virtual double	alphar (double tau, double delta, const std::vector< double > &x, std::size_t itau, std::size_t idelta)
	The residual non-dimensionalized Helmholtz energy \(\alpha^r\). More...

virtual double	d_alphar_dxi (double tau, double delta, const std::vector< double > &x, std::size_t itau, std::size_t idelta, std::size_t i, bool xN_independent)
	The first composition derivative of \(\alpha^r\) as well as derivatives with respect to \(\tau\) and \(\delta\). More...

virtual double	d2_alphar_dxidxj (double tau, double delta, const std::vector< double > &x, std::size_t itau, std::size_t idelta, std::size_t i, std::size_t j, bool xN_independent)
	The second composition derivative of \(\alpha^r\) as well as derivatives with respect to \(\tau\) and \(\delta\). More...

virtual double	d3_alphar_dxidxjdxk (double tau, double delta, const std::vector< double > &x, std::size_t itau, std::size_t idelta, std::size_t i, std::size_t j, std::size_t k, bool xN_independent)
	The third composition derivative of \(\alpha^r\) as well as derivatives with respect to \(\tau\) and \(\delta\). More...

virtual double	am_term (double tau, const std::vector< double > &x, std::size_t itau)
	The n-th derivative of \(a_m\) with respect to \(\tau\). More...

virtual double	d_am_term_dxi (double tau, const std::vector< double > &x, std::size_t itau, std::size_t i, bool xN_independent)
	The first composition derivative of \(a_m\) as well as derivatives with respect to \(\tau\). More...

virtual double	d2_am_term_dxidxj (double tau, const std::vector< double > &x, std::size_t itau, std::size_t i, std::size_t j, bool xN_independent)
	The second composition derivative of \(a_m\) as well as derivatives with respect to \(\tau\). More...

virtual double	d3_am_term_dxidxjdxk (double tau, const std::vector< double > &x, std::size_t itau, std::size_t i, std::size_t j, std::size_t k, bool xN_independent)
	The third composition derivative of \(a_m\) as well as derivatives with respect to \(\tau\). More...

virtual double	bm_term (const std::vector< double > &x)
	The term \(b_{\rm m}\) (mixture co-volume) More...

virtual double	d_bm_term_dxi (const std::vector< double > &x, std::size_t i, bool xN_independent)
	The first composition derivative of \(b_m\). More...

virtual double	d2_bm_term_dxidxj (const std::vector< double > &x, std::size_t i, std::size_t j, bool xN_independent)
	The second composition derivative of \(b_m\). More...

virtual double	d3_bm_term_dxidxjdxk (const std::vector< double > &x, std::size_t i, std::size_t j, std::size_t k, bool xN_independent)
	The third composition derivative of \(b_m\). More...

virtual double	cm_term ()
	The term \(c_{\rm m}\) (volume translation) More...

void	set_cm (double val)
	Set the volume translation parameter. More...

double	get_cm ()
	Get the volume translation parameter. More...

virtual void	set_Q_k (const size_t sgi, const double value)
	Modify the surface parameter Q_k of the sub group sgi. More...

virtual double	get_Q_k (const size_t sgi) const
	Retrieve the surface parameter Q_k of the sub group sgi. More...

double	aij_term (double tau, std::size_t i, std::size_t j, std::size_t itau)
	The n-th \(\tau\) derivative of \(a_{ij}(\tau)\). More...

double	u_term (double tau, std::size_t i, std::size_t j, std::size_t itau)

double	aii_term (double tau, std::size_t i, std::size_t itau)

double	psi_minus (double delta, const std::vector< double > &x, std::size_t itau, std::size_t idelta)
	The term \( \psi^{(-)}\) and its \(\tau\) and \( \delta \) derivatives. More...

double	d_psi_minus_dxi (double delta, const std::vector< double > &x, std::size_t itau, std::size_t idelta, std::size_t i, bool xN_independent)
	The third composition derivative of \( \psi^{(-)}\) and its \( \delta \) derivatives. More...

double	d2_psi_minus_dxidxj (double delta, const std::vector< double > &x, std::size_t itau, std::size_t idelta, std::size_t i, std::size_t j, bool xN_independent)
	The second composition derivative of \( \psi^{(-)}\) and its \( \delta \) derivatives. More...

double	d3_psi_minus_dxidxjdxk (double delta, const std::vector< double > &x, std::size_t itau, std::size_t idelta, std::size_t i, std::size_t j, std::size_t k, bool xN_independent)
	The third composition derivative of \( \psi^{(-)}\) and its \( \delta \) derivatives. More...

double	PI_12 (double delta, const std::vector< double > &x, std::size_t idelta)
	The term \( \Pi_{12}\) and its \( \delta \) derivatives. More...

double	d_PI_12_dxi (double delta, const std::vector< double > &x, std::size_t idelta, std::size_t i, bool xN_independent)
	The first composition derivative of \( \Pi_{12}\) and its \( \delta \) derivatives. More...

double	d2_PI_12_dxidxj (double delta, const std::vector< double > &x, std::size_t idelta, std::size_t i, std::size_t j, bool xN_independent)
	The second composition derivative of \( \Pi_{12}\) and its \( \delta \) derivatives. More...

double	d3_PI_12_dxidxjdxk (double delta, const std::vector< double > &x, std::size_t idelta, std::size_t i, std::size_t j, std::size_t k, bool xN_independent)
	The third composition derivative of \( \Pi_{12}\) and its \( \delta \) derivatives. More...

double	tau_times_a (double tau, const std::vector< double > &x, std::size_t itau)
	The term \( \tau\cdot a_m(\tau)\) and its \( \tau \) derivatives. More...

double	d_tau_times_a_dxi (double tau, const std::vector< double > &x, std::size_t itau, std::size_t i, bool xN_independent)
	The first composition derivative of \( \tau\cdot a_m(\tau)\) and its \( \tau \) derivatives. More...

double	d2_tau_times_a_dxidxj (double tau, const std::vector< double > &x, std::size_t itau, std::size_t i, std::size_t j, bool xN_independent)
	The second composition derivative of \( \tau\cdot a_m(\tau)\) and its \( \tau \) derivatives. More...

double	d3_tau_times_a_dxidxjdxk (double tau, const std::vector< double > &x, std::size_t itau, std::size_t i, std::size_t j, std::size_t k, bool xN_independent)
	The third composition derivative of \( \tau\cdot a_m(\tau)\) and its \( \tau \) derivatives. More...

double	psi_plus (double delta, const std::vector< double > &x, std::size_t idelta)
	The term \( \psi^{(+)}\) and its \( \delta \) derivatives. More...

double	d_psi_plus_dxi (double delta, const std::vector< double > &x, std::size_t idelta, std::size_t i, bool xN_independent)
	The first composition derivative of \( \psi^{(+)}\) and its \( \delta \) derivatives. More...

double	d2_psi_plus_dxidxj (double delta, const std::vector< double > &x, std::size_t idelta, std::size_t i, std::size_t j, bool xN_independent)
	The second composition derivative of \( \psi^{(+)}\) and its \( \delta \) derivatives. More...

double	d3_psi_plus_dxidxjdxk (double delta, const std::vector< double > &x, std::size_t idelta, std::size_t i, std::size_t j, std::size_t k, bool xN_independent)
	The third composition derivative of \( \psi^{(+)}\) and its \( \delta \) derivatives. More...

double	c_term (const std::vector< double > &x)
	The term \(c\) used in the pure composition partial derivatives of \(\psi^{(+)}\). More...

double	d_c_term_dxi (const std::vector< double > &x, std::size_t i, bool xN_independent)
	The first composition derivative of the term \(c\) used in the pure composition partial derivatives of \(\psi^{(+)}\). More...

double	d2_c_term_dxidxj (const std::vector< double > &x, std::size_t i, std::size_t j, bool xN_independent)
	The second composition derivative of the term \(c\) used in the pure composition partial derivatives of \(\psi^{(+)}\). More...

double	d3_c_term_dxidxjdxk (const std::vector< double > &x, std::size_t i, std::size_t j, std::size_t k, bool xN_independent)
	The third composition derivative of the term \(c\) used in the pure composition partial derivatives of \(\psi^{(+)}\). More...

double	A_term (double delta, const std::vector< double > &x)
	The term \(A\) used in the pure composition partial derivatives of \(\psi^{(+)}\). More...

double	d_A_term_dxi (double delta, const std::vector< double > &x, std::size_t i, bool xN_independent)
	The first composition derivative of the term \(A\) used in the pure composition partial derivatives of \(\psi^{(+)}\). More...

double	d2_A_term_dxidxj (double delta, const std::vector< double > &x, std::size_t i, std::size_t j, bool xN_independent)
	The second composition derivative of the term \(A\) used in the pure composition partial derivatives of \(\psi^{(+)}\). More...

double	d3_A_term_dxidxjdxk (double delta, const std::vector< double > &x, std::size_t i, std::size_t j, std::size_t k, bool xN_independent)
	The third composition derivative of the term \(A\) used in the pure composition partial derivatives of \(\psi^{(+)}\). More...

virtual void	set_interaction_parameter (const std::size_t mgi1, const std::size_t mgi2, const std::string &parameter, const double value)

virtual double	get_interaction_parameter (const std::size_t mgi1, const std::size_t mgi2, const std::string &parameter)

Protected Member Functions
void	_ensure_aii_cache (double tau) const

Protected Attributes
double	rho_r
	The reducing density to be used [mol/m3]. More...

double	T_r
	The reducing temperature to be used [K]. More...

std::vector< double >	Tc
	Vector of critical temperatures (in K) More...

std::vector< double >	pc
	Vector of critical pressures (in Pa) More...

std::vector< double >	acentric
	Vector of acentric factors (unitless) More...

double	R_u
	The universal gas constant in J/(mol*K) More...

double	Delta_1
	The first cubic constant. More...

double	Delta_2
	The second cubic constant. More...

int	N
	Number of components in the mixture. More...

std::vector< std::vector< double > >	k
	The interaction parameters (k_ii = 0) More...

double	cm
	The volume translation parameter. More...

std::vector< shared_ptr< AbstractCubicAlphaFunction > >	alpha

double	m_tau_cache
	Cache: aii_term values for the most recent tau. Populated lazily by _ensure_aii_cache(). More...

std::vector< std::array< double, 5 > >	m_aii_cache

std::vector< unsigned long >	m_alpha_versions_cache

std::vector< double >	m_b0_ii_cache

Constructor & Destructor Documentation

◆ AbstractCubic()

AbstractCubic::AbstractCubic	(	const std::vector< double > &	Tc,
		std::vector< double >	pc,
		std::vector< double >	acentric,
		double	R_u,
		double	Delta_1,
		double	Delta_2,
		const std::vector< double > &	C1 = `std::vector<double>()`,
		const std::vector< double > &	C2 = `std::vector<double>()`,
		const std::vector< double > &	C3 = `std::vector<double>()`
	)

The abstract base clase for the concrete implementations of the cubic equations of state.

This abstract base class describes the structure that must be implemented by concrete implementations of the cubic equations of state (SRK, PR, etc.). The virtual functions must be implemented by the derived classes, the remaining functions are generic and are not dependent on the equation of state, so long as it has the formulation given in this work.

Definition at line 196 of file GeneralizedCubic.cpp.

◆ ~AbstractCubic()

virtual AbstractCubic::~AbstractCubic ( )

virtualdefault

Member Function Documentation

◆ _ensure_aii_cache()

void AbstractCubic::_ensure_aii_cache ( double tau ) const

inlineprotected

Definition at line 135 of file GeneralizedCubic.h.

◆ a0_ii()

virtual double AbstractCubic::a0_ii ( std::size_t i )

pure virtual

Get the leading constant in the expression for the pure fluid attractive energy term (must be implemented by derived classes)

Implemented in PengRobinson, and SRK.

◆ A_term()

double AbstractCubic::A_term	(	double	delta,
		const std::vector< double > &	x
	)

inline

The term \(A\) used in the pure composition partial derivatives of \(\psi^{(+)}\).

\[ A = \log\left(\frac{\Delta_1\delta\rho_r b_m+1}{\Delta_2\delta\rho_r b+1}\right) \]

Parameters

delta	The reduced density \(\delta = \frac{\rho}{\rho_c}\)
x	The vector of mole fractions

Definition at line 619 of file GeneralizedCubic.h.

◆ aii_term()

double AbstractCubic::aii_term	(	double	tau,
		std::size_t	i,
		std::size_t	itau
	)

Take the n-th tau derivative of the \(a_{ii}(\tau)\) pure fluid contribution

Parameters

tau	The reciprocal reduced temperature \(\tau=T_r/T\)
i	The index of the component
itau	The number of derivatives of \(u\) to take with respect to \(\tau\) (itau=0 is just a_{ij}, itau=1 is d(a_ij)/d(tau), etc.)

Definition at line 311 of file GeneralizedCubic.cpp.

◆ aij_term()

double AbstractCubic::aij_term	(	double	tau,
		std::size_t	i,
		std::size_t	j,
		std::size_t	itau
	)

The n-th \(\tau\) derivative of \(a_{ij}(\tau)\).

Parameters

tau	The reciprocal reduced temperature \(\tau=T_r/T\)
i	The first index
j	The second index
itau	The number of derivatives of \(a_{ij}\) to take with respect to \(\tau\) (itau=0 is just a_{ij}, itau=1 is d(a_ij)/d(tau), etc.)

Definition at line 344 of file GeneralizedCubic.cpp.

◆ alphar()

double AbstractCubic::alphar	(	double	tau,
		double	delta,
		const std::vector< double > &	x,
		std::size_t	itau,
		std::size_t	idelta
	)

virtual

The residual non-dimensionalized Helmholtz energy \(\alpha^r\).

Definition at line 733 of file GeneralizedCubic.cpp.

◆ am_term()

double AbstractCubic::am_term	(	double	tau,
		const std::vector< double > &	x,
		std::size_t	itau
	)

virtual

The n-th derivative of \(a_m\) with respect to \(\tau\).

Parameters

tau	The reciprocal reduced temperature \(\tau=T_r/T\)
x	The vector of mole fractions
itau	The number of derivatives of \(a_m\) to take with respect to \(\tau\) (itau=0 is just a_m, itau=1 is d(a_m)/d(tau), etc.)

Reimplemented in VTPRCubic.

Definition at line 232 of file GeneralizedCubic.cpp.

◆ b0_ii()

virtual double AbstractCubic::b0_ii ( std::size_t i )

pure virtual

Get the leading constant in the expression for the pure fluid covolume term (must be implemented by derived classes)

Implemented in PengRobinson, and SRK.

◆ bm_term()

double AbstractCubic::bm_term ( const std::vector< double > & x )

virtual

The term \(b_{\rm m}\) (mixture co-volume)

Parameters

x	The vector of mole fractions

Reimplemented in VTPRCubic.

Definition at line 277 of file GeneralizedCubic.cpp.

◆ c_term()

double AbstractCubic::c_term ( const std::vector< double > & x )

inline

The term \(c\) used in the pure composition partial derivatives of \(\psi^{(+)}\).

\(c\) is given by

\[ c = \frac{1}{b_m} \]

Parameters

x	The vector of mole fractions

Definition at line 566 of file GeneralizedCubic.h.

◆ cm_term()

double AbstractCubic::cm_term ( )

virtual

The term \(c_{\rm m}\) (volume translation)

Definition at line 307 of file GeneralizedCubic.cpp.

◆ d2_A_term_dxidxj()

double AbstractCubic::d2_A_term_dxidxj	(	double	delta,
		const std::vector< double > &	x,
		std::size_t	i,
		std::size_t	j,
		bool	xN_independent
	)

inline

The second composition derivative of the term \(A\) used in the pure composition partial derivatives of \(\psi^{(+)}\).

Parameters

delta	The reduced density \(\delta = \frac{\rho}{\rho_c}\)
x	The vector of mole fractions
i	The first index
j	The second index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 643 of file GeneralizedCubic.h.

◆ d2_alphar_dxidxj()

double AbstractCubic::d2_alphar_dxidxj	(	double	tau,
		double	delta,
		const std::vector< double > &	x,
		std::size_t	itau,
		std::size_t	idelta,
		std::size_t	i,
		std::size_t	j,
		bool	xN_independent
	)

virtual

The second composition derivative of \(\alpha^r\) as well as derivatives with respect to \(\tau\) and \(\delta\).

Definition at line 743 of file GeneralizedCubic.cpp.

◆ d2_am_term_dxidxj()

double AbstractCubic::d2_am_term_dxidxj	(	double	tau,
		const std::vector< double > &	x,
		std::size_t	itau,
		std::size_t	i,
		std::size_t	j,
		bool	xN_independent
	)

virtual

The second composition derivative of \(a_m\) as well as derivatives with respect to \(\tau\).

Parameters

tau	The reciprocal reduced temperature \(\tau=T_r/T\)
x	The vector of mole fractions
itau	The number of derivatives of \(a_m\) to take with respect to \(\tau\) (itau=0 is just a_m, itau=1 is d(a_m)/d(tau), etc.)
i	The first index
j	The second index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Reimplemented in VTPRCubic.

Definition at line 262 of file GeneralizedCubic.cpp.

◆ d2_bm_term_dxidxj()

double AbstractCubic::d2_bm_term_dxidxj	(	const std::vector< double > &	x,
		std::size_t	i,
		std::size_t	j,
		bool	xN_independent
	)

virtual

The second composition derivative of \(b_m\).

Parameters

x	The vector of mole fractions
i	The first index
j	The second index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Reimplemented in VTPRCubic.

Definition at line 300 of file GeneralizedCubic.cpp.

◆ d2_c_term_dxidxj()

double AbstractCubic::d2_c_term_dxidxj	(	const std::vector< double > &	x,
		std::size_t	i,
		std::size_t	j,
		bool	xN_independent
	)

inline

The second composition derivative of the term \(c\) used in the pure composition partial derivatives of \(\psi^{(+)}\).

Parameters

x	The vector of mole fractions
i	The first index
j	The second index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 585 of file GeneralizedCubic.h.

◆ d2_PI_12_dxidxj()

double AbstractCubic::d2_PI_12_dxidxj	(	double	delta,
		const std::vector< double > &	x,
		std::size_t	idelta,
		std::size_t	i,
		std::size_t	j,
		bool	xN_independent
	)

The second composition derivative of \( \Pi_{12}\) and its \( \delta \) derivatives.

Parameters

delta	The reduced density \(\delta = \frac{\rho}{\rho_c}\)
x	The vector of mole fractions
idelta	How many derivatives to take with respect to \(\delta\)
i	The first index
j	The second index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 507 of file GeneralizedCubic.cpp.

◆ d2_psi_minus_dxidxj()

double AbstractCubic::d2_psi_minus_dxidxj	(	double	delta,
		const std::vector< double > &	x,
		std::size_t	itau,
		std::size_t	idelta,
		std::size_t	i,
		std::size_t	j,
		bool	xN_independent
	)

The second composition derivative of \( \psi^{(-)}\) and its \( \delta \) derivatives.

Parameters

delta	The reduced density \(\delta = \frac{\rho}{\rho_c}\)
x	The vector of mole fractions
itau	How many derivatives to take with respect to \(\tau\)
idelta	How many derivatives to take with respect to \(\delta\)
i	The first index
j	The second index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 424 of file GeneralizedCubic.cpp.

◆ d2_psi_plus_dxidxj()

double AbstractCubic::d2_psi_plus_dxidxj	(	double	delta,
		const std::vector< double > &	x,
		std::size_t	idelta,
		std::size_t	i,
		std::size_t	j,
		bool	xN_independent
	)

The second composition derivative of \( \psi^{(+)}\) and its \( \delta \) derivatives.

Parameters

delta	The reduced density \(\delta = \frac{\rho}{\rho_c}\)
x	The vector of mole fractions
idelta	How many derivatives to take with respect to \(\delta\)
i	The first index
j	The second index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 610 of file GeneralizedCubic.cpp.

◆ d2_tau_times_a_dxidxj()

double AbstractCubic::d2_tau_times_a_dxidxj	(	double	tau,
		const std::vector< double > &	x,
		std::size_t	itau,
		std::size_t	i,
		std::size_t	j,
		bool	xN_independent
	)

The second composition derivative of \( \tau\cdot a_m(\tau)\) and its \( \tau \) derivatives.

Parameters

tau	The reciprocal reduced temperature \(\tau = \frac{T_c}{T}\)
x	The vector of mole fractions
itau	How many derivatives to take with respect to \(\tau\)
i	The first index
j	The second index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 716 of file GeneralizedCubic.cpp.

◆ d3_A_term_dxidxjdxk()

double AbstractCubic::d3_A_term_dxidxjdxk	(	double	delta,
		const std::vector< double > &	x,
		std::size_t	i,
		std::size_t	j,
		std::size_t	k,
		bool	xN_independent
	)

inline

The third composition derivative of the term \(A\) used in the pure composition partial derivatives of \(\psi^{(+)}\).

Parameters

delta	The reduced density \(\delta = \frac{\rho}{\rho_c}\)
x	The vector of mole fractions
i	The first index
j	The second index
k	The third index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 659 of file GeneralizedCubic.h.

◆ d3_alphar_dxidxjdxk()

double AbstractCubic::d3_alphar_dxidxjdxk	(	double	tau,
		double	delta,
		const std::vector< double > &	x,
		std::size_t	itau,
		std::size_t	idelta,
		std::size_t	i,
		std::size_t	j,
		std::size_t	k,
		bool	xN_independent
	)

virtual

The third composition derivative of \(\alpha^r\) as well as derivatives with respect to \(\tau\) and \(\delta\).

Definition at line 752 of file GeneralizedCubic.cpp.

◆ d3_am_term_dxidxjdxk()

double AbstractCubic::d3_am_term_dxidxjdxk	(	double	tau,
		const std::vector< double > &	x,
		std::size_t	itau,
		std::size_t	i,
		std::size_t	j,
		std::size_t	k,
		bool	xN_independent
	)

virtual

The third composition derivative of \(a_m\) as well as derivatives with respect to \(\tau\).

Parameters

tau	The reciprocal reduced temperature \(\tau=T_r/T\)
x	The vector of mole fractions
itau	The number of derivatives of \(a_m\) to take with respect to \(\tau\) (itau=0 is just a_m, itau=1 is d(a_m)/d(tau), etc.)
i	The first index
j	The second index
k	The third index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Reimplemented in VTPRCubic.

Definition at line 272 of file GeneralizedCubic.cpp.

◆ d3_bm_term_dxidxjdxk()

double AbstractCubic::d3_bm_term_dxidxjdxk	(	const std::vector< double > &	x,
		std::size_t	i,
		std::size_t	j,
		std::size_t	k,
		bool	xN_independent
	)

virtual

The third composition derivative of \(b_m\).

Parameters

x	The vector of mole fractions
i	The first index
j	The second index
k	The third index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Reimplemented in VTPRCubic.

Definition at line 303 of file GeneralizedCubic.cpp.

◆ d3_c_term_dxidxjdxk()

double AbstractCubic::d3_c_term_dxidxjdxk	(	const std::vector< double > &	x,
		std::size_t	i,
		std::size_t	j,
		std::size_t	k,
		bool	xN_independent
	)

inline

The third composition derivative of the term \(c\) used in the pure composition partial derivatives of \(\psi^{(+)}\).

Parameters

x	The vector of mole fractions
i	The first index
j	The second index
k	The third index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 598 of file GeneralizedCubic.h.

◆ d3_PI_12_dxidxjdxk()

double AbstractCubic::d3_PI_12_dxidxjdxk	(	double	delta,
		const std::vector< double > &	x,
		std::size_t	idelta,
		std::size_t	i,
		std::size_t	j,
		std::size_t	k,
		bool	xN_independent
	)

The third composition derivative of \( \Pi_{12}\) and its \( \delta \) derivatives.

Parameters

delta	The reduced density \(\delta = \frac{\rho}{\rho_c}\)
x	The vector of mole fractions
idelta	How many derivatives to take with respect to \(\delta\)
i	The first index
j	The second index
k	The third index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 533 of file GeneralizedCubic.cpp.

◆ d3_psi_minus_dxidxjdxk()

double AbstractCubic::d3_psi_minus_dxidxjdxk	(	double	delta,
		const std::vector< double > &	x,
		std::size_t	itau,
		std::size_t	idelta,
		std::size_t	i,
		std::size_t	j,
		std::size_t	k,
		bool	xN_independent
	)

The third composition derivative of \( \psi^{(-)}\) and its \( \delta \) derivatives.

Parameters

delta	The reduced density \(\delta = \frac{\rho}{\rho_c}\)
x	The vector of mole fractions
itau	How many derivatives to take with respect to \(\tau\)
idelta	How many derivatives to take with respect to \(\delta\)
i	The first index
j	The second index
k	The third index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 450 of file GeneralizedCubic.cpp.

◆ d3_psi_plus_dxidxjdxk()

double AbstractCubic::d3_psi_plus_dxidxjdxk	(	double	delta,
		const std::vector< double > &	x,
		std::size_t	idelta,
		std::size_t	i,
		std::size_t	j,
		std::size_t	k,
		bool	xN_independent
	)

The third composition derivative of \( \psi^{(+)}\) and its \( \delta \) derivatives.

Parameters

delta	The reduced density \(\delta = \frac{\rho}{\rho_c}\)
x	The vector of mole fractions
idelta	How many derivatives to take with respect to \(\delta\)
i	The first index
j	The second index
k	The third index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 674 of file GeneralizedCubic.cpp.

◆ d3_tau_times_a_dxidxjdxk()

double AbstractCubic::d3_tau_times_a_dxidxjdxk	(	double	tau,
		const std::vector< double > &	x,
		std::size_t	itau,
		std::size_t	i,
		std::size_t	j,
		std::size_t	k,
		bool	xN_independent
	)

The third composition derivative of \( \tau\cdot a_m(\tau)\) and its \( \tau \) derivatives.

Parameters

tau	The reciprocal reduced temperature \(\tau = \frac{T_c}{T}\)
x	The vector of mole fractions
itau	How many derivatives to take with respect to \(\tau\)
i	The first index
j	The second index
k	The third index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 724 of file GeneralizedCubic.cpp.

◆ d_A_term_dxi()

double AbstractCubic::d_A_term_dxi	(	double	delta,
		const std::vector< double > &	x,
		std::size_t	i,
		bool	xN_independent
	)

inline

The first composition derivative of the term \(A\) used in the pure composition partial derivatives of \(\psi^{(+)}\).

Parameters

delta	The reduced density \(\delta = \frac{\rho}{\rho_c}\)
x	The vector of mole fractions
i	The first index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 631 of file GeneralizedCubic.h.

◆ d_alphar_dxi()

double AbstractCubic::d_alphar_dxi	(	double	tau,
		double	delta,
		const std::vector< double > &	x,
		std::size_t	itau,
		std::size_t	idelta,
		std::size_t	i,
		bool	xN_independent
	)

virtual

The first composition derivative of \(\alpha^r\) as well as derivatives with respect to \(\tau\) and \(\delta\).

Definition at line 736 of file GeneralizedCubic.cpp.

◆ d_am_term_dxi()

double AbstractCubic::d_am_term_dxi	(	double	tau,
		const std::vector< double > &	x,
		std::size_t	itau,
		std::size_t	i,
		bool	xN_independent
	)

virtual

The first composition derivative of \(a_m\) as well as derivatives with respect to \(\tau\).

Parameters

tau	The reciprocal reduced temperature \(\tau=T_r/T\)
x	The vector of mole fractions
itau	The number of derivatives of \(a_m\) to take with respect to \(\tau\) (itau=0 is just a_m, itau=1 is d(a_m)/d(tau), etc.)
i	The first index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Reimplemented in VTPRCubic.

Definition at line 246 of file GeneralizedCubic.cpp.

◆ d_bm_term_dxi()

double AbstractCubic::d_bm_term_dxi	(	const std::vector< double > &	x,
		std::size_t	i,
		bool	xN_independent
	)

virtual

The first composition derivative of \(b_m\).

Parameters

x	The vector of mole fractions
i	The first index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Reimplemented in VTPRCubic.

Definition at line 293 of file GeneralizedCubic.cpp.

◆ d_c_term_dxi()

double AbstractCubic::d_c_term_dxi	(	const std::vector< double > &	x,
		std::size_t	i,
		bool	xN_independent
	)

inline

The first composition derivative of the term \(c\) used in the pure composition partial derivatives of \(\psi^{(+)}\).

Parameters

x	The vector of mole fractions
i	The first index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 575 of file GeneralizedCubic.h.

◆ d_PI_12_dxi()

double AbstractCubic::d_PI_12_dxi	(	double	delta,
		const std::vector< double > &	x,
		std::size_t	idelta,
		std::size_t	i,
		bool	xN_independent
	)

The first composition derivative of \( \Pi_{12}\) and its \( \delta \) derivatives.

Parameters

delta	The reduced density \(\delta = \frac{\rho}{\rho_c}\)
x	The vector of mole fractions
idelta	How many derivatives to take with respect to \(\delta\)
i	The first index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 488 of file GeneralizedCubic.cpp.

◆ d_psi_minus_dxi()

double AbstractCubic::d_psi_minus_dxi	(	double	delta,
		const std::vector< double > &	x,
		std::size_t	itau,
		std::size_t	idelta,
		std::size_t	i,
		bool	xN_independent
	)

The third composition derivative of \( \psi^{(-)}\) and its \( \delta \) derivatives.

Parameters

delta	The reduced density \(\delta = \frac{\rho}{\rho_c}\)
x	The vector of mole fractions
itau	How many derivatives to take with respect to \(\tau\)
idelta	How many derivatives to take with respect to \(\delta\)
i	The first index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 402 of file GeneralizedCubic.cpp.

◆ d_psi_plus_dxi()

double AbstractCubic::d_psi_plus_dxi	(	double	delta,
		const std::vector< double > &	x,
		std::size_t	idelta,
		std::size_t	i,
		bool	xN_independent
	)

The first composition derivative of \( \psi^{(+)}\) and its \( \delta \) derivatives.

Parameters

delta	The reduced density \(\delta = \frac{\rho}{\rho_c}\)
x	The vector of mole fractions
idelta	How many derivatives to take with respect to \(\delta\)
i	The first index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 576 of file GeneralizedCubic.cpp.

◆ d_tau_times_a_dxi()

double AbstractCubic::d_tau_times_a_dxi	(	double	tau,
		const std::vector< double > &	x,
		std::size_t	itau,
		std::size_t	i,
		bool	xN_independent
	)

The first composition derivative of \( \tau\cdot a_m(\tau)\) and its \( \tau \) derivatives.

Parameters

tau	The reciprocal reduced temperature \(\tau = \frac{T_c}{T}\)
x	The vector of mole fractions
itau	How many derivatives to take with respect to \(\tau\)
i	The first index
xN_independent	True if \(x_N\) is an independent variable, false otherwise (dependent on other \(N-1\) mole fractions)

Definition at line 709 of file GeneralizedCubic.cpp.

◆ get_acentric()

std::vector< double > & AbstractCubic::get_acentric ( )

inline

Get the vector of acentric factors.

Definition at line 217 of file GeneralizedCubic.h.

◆ get_all_alpha_functions()

const std::vector< shared_ptr< AbstractCubicAlphaFunction > > & AbstractCubic::get_all_alpha_functions ( )

inline

Get all the alpha functions.

Definition at line 182 of file GeneralizedCubic.h.

◆ get_alpha_function()

shared_ptr< AbstractCubicAlphaFunction > AbstractCubic::get_alpha_function ( std::size_t i )

inline

Get the alpha function for the i-th component.

Definition at line 178 of file GeneralizedCubic.h.

◆ get_cm()

double AbstractCubic::get_cm ( )

inline

Get the volume translation parameter.

Definition at line 358 of file GeneralizedCubic.h.

◆ get_Delta_1()

double AbstractCubic::get_Delta_1 ( )

inline

Read-only accessor for value of Delta_1.

Definition at line 221 of file GeneralizedCubic.h.

◆ get_Delta_2()

double AbstractCubic::get_Delta_2 ( )

inline

Read-only accessor for value of Delta_2.

Definition at line 225 of file GeneralizedCubic.h.

◆ get_interaction_parameter()

virtual double AbstractCubic::get_interaction_parameter	(	const std::size_t	mgi1,
		const std::size_t	mgi2,
		const std::string &	parameter
	)

inlinevirtual

Reimplemented in VTPRCubic.

Definition at line 678 of file GeneralizedCubic.h.

◆ get_kij()

double AbstractCubic::get_kij	(	std::size_t	i,
		std::size_t	j
	)

inline

Get the kij factor for the ij pair.

Definition at line 205 of file GeneralizedCubic.h.

◆ get_kmat()

const std::vector< std::vector< double > > & AbstractCubic::get_kmat ( )

inline

Get the entire kij matrix in one shot.

Definition at line 192 of file GeneralizedCubic.h.

◆ get_pc()

std::vector< double > & AbstractCubic::get_pc ( )

inline

Get the vector of critical pressures (in Pa)

Definition at line 213 of file GeneralizedCubic.h.

◆ get_Q_k()

virtual double AbstractCubic::get_Q_k ( const size_t sgi ) const

inlinevirtual

Retrieve the surface parameter Q_k of the sub group sgi.

Reimplemented in VTPRCubic.

Definition at line 367 of file GeneralizedCubic.h.

◆ get_R_u()

double AbstractCubic::get_R_u ( )

inline

Read-only accessor for value of R_u (universal gas constant)

Definition at line 229 of file GeneralizedCubic.h.

◆ get_rhor()

double AbstractCubic::get_rhor ( )

inline

Get the reducing density to be used.

Definition at line 249 of file GeneralizedCubic.h.

◆ get_Tc()

std::vector< double > & AbstractCubic::get_Tc ( )

inline

Get the vector of critical temperatures (in K)

Definition at line 209 of file GeneralizedCubic.h.

◆ get_Tr()

double AbstractCubic::get_Tr ( )

inline

Get the reducing temperature to be used.

Definition at line 245 of file GeneralizedCubic.h.

◆ m_ii()

virtual double AbstractCubic::m_ii ( std::size_t i )

pure virtual

Get the m_ii variable in the alpha term inculuded in the attractive part.

Implemented in PengRobinson, and SRK.

◆ PI_12()

double AbstractCubic::PI_12	(	double	delta,
		const std::vector< double > &	x,
		std::size_t	idelta
	)

The term \( \Pi_{12}\) and its \( \delta \) derivatives.

Parameters

delta	The reduced density \(\delta = \frac{\rho}{\rho_c}\)
x	The vector of mole fractions
idelta	How many derivatives to take with respect to \(\delta\)

\[ \Pi_{12} = (1+\Delta_1\bm\rhor \delta)(1+\Delta_2\bm\rhor \delta) \]

Definition at line 470 of file GeneralizedCubic.cpp.

◆ psi_minus()

double AbstractCubic::psi_minus	(	double	delta,
		const std::vector< double > &	x,
		std::size_t	itau,
		std::size_t	idelta
	)

The term \( \psi^{(-)}\) and its \(\tau\) and \( \delta \) derivatives.

Parameters

delta	The reduced density \(\delta = \frac{\rho}{\rho_c}\)
x	The vector of mole fractions
itau	How many derivatives to take with respect to \(\tau\)
idelta	How many derivatives to take with respect to \(\delta\)

Definition at line 376 of file GeneralizedCubic.cpp.

◆ psi_plus()

double AbstractCubic::psi_plus	(	double	delta,
		const std::vector< double > &	x,
		std::size_t	idelta
	)

The term \( \psi^{(+)}\) and its \( \delta \) derivatives.

Parameters

delta	The reduced density \(\delta = \frac{\rho}{\rho_c}\)
x	The vector of mole fractions
idelta	How many derivatives to take with respect to \(\delta\)

\[ \psi^{(+)} = \dfrac{\ln\left(\dfrac{\Delta_1\bm\rhor \delta+1}{\Delta_2\bm\rhor \delta+1}\right)}{\bm(\Delta_1-\Delta_2)} \]

Definition at line 553 of file GeneralizedCubic.cpp.

◆ set_all_alpha_functions()

void AbstractCubic::set_all_alpha_functions ( const std::vector< shared_ptr< AbstractCubicAlphaFunction > > & alpha )

inline

Set all the alpha functions.

Definition at line 186 of file GeneralizedCubic.h.

◆ set_alpha()

void AbstractCubic::set_alpha	(	const std::vector< double > &	C1,
		const std::vector< double > &	C2,
		const std::vector< double > &	C3
	)

Set the constants for the Mathias-Copeman alpha function, or if C1,C2,C3 are all empty, set the default alpha model.

Resize the vector of alpha functions

If no Mathias-Copeman coefficients are passed in (all empty vectors), use the predictive scheme for m_ii

Use the Mathias-Copeman constants passed in to initialize Mathias-Copeman alpha functions

Definition at line 215 of file GeneralizedCubic.cpp.

◆ set_alpha_function()

void AbstractCubic::set_alpha_function	(	std::size_t	i,
		shared_ptr< AbstractCubicAlphaFunction > &	acaf
	)

inline

Set the alpha function for the i-th component.

Definition at line 173 of file GeneralizedCubic.h.

◆ set_C_MC()

void AbstractCubic::set_C_MC	(	std::size_t	i,
		double	c1,
		double	c2,
		double	c3
	)

inline

Set the three Mathias-Copeman constants in one shot for the component i of a mixture.

Definition at line 254 of file GeneralizedCubic.h.

◆ set_C_Twu()

void AbstractCubic::set_C_Twu	(	std::size_t	i,
		double	L,
		double	M,
		double	N
	)

inline

Set the three Twu constants in one shot for the component i of a mixture.

Definition at line 259 of file GeneralizedCubic.h.

◆ set_cm()

void AbstractCubic::set_cm ( double val )

inline

Set the volume translation parameter.

Definition at line 354 of file GeneralizedCubic.h.

◆ set_interaction_parameter()

virtual void AbstractCubic::set_interaction_parameter	(	const std::size_t	mgi1,
		const std::size_t	mgi2,
		const std::string &	parameter,
		const double	value
	)

inlinevirtual

Reimplemented in VTPRCubic.

Definition at line 674 of file GeneralizedCubic.h.

◆ set_kij()

void AbstractCubic::set_kij	(	std::size_t	i,
		std::size_t	j,
		double	val
	)

inline

Set the kij factor for the ij pair.

Definition at line 200 of file GeneralizedCubic.h.

◆ set_kmat()

void AbstractCubic::set_kmat ( const std::vector< std::vector< double > > & k )

inline

Set the entire kij matrix in one shot.

Definition at line 196 of file GeneralizedCubic.h.

◆ set_Q_k()

virtual void AbstractCubic::set_Q_k	(	const size_t	sgi,
		const double	value
	)

inlinevirtual

Modify the surface parameter Q_k of the sub group sgi.

Reimplemented in VTPRCubic.

Definition at line 363 of file GeneralizedCubic.h.

◆ set_rhor()

void AbstractCubic::set_rhor ( double rhor )

inline

Set the reducing density to be used.

Definition at line 241 of file GeneralizedCubic.h.

◆ set_Tr()

void AbstractCubic::set_Tr ( double Tr )

inline

Set the reducing temperature to be used.

Definition at line 233 of file GeneralizedCubic.h.

◆ tau_times_a()

double AbstractCubic::tau_times_a	(	double	tau,
		const std::vector< double > &	x,
		std::size_t	itau
	)

The term \( \tau\cdot a_m(\tau)\) and its \( \tau \) derivatives.

Parameters

tau	The reciprocal reduced temperature \(\tau = \frac{T_c}{T}\)
x	The vector of mole fractions
itau	How many derivatives to take with respect to \(\tau\)

Definition at line 702 of file GeneralizedCubic.cpp.

◆ u_term()

double AbstractCubic::u_term	(	double	tau,
		std::size_t	i,
		std::size_t	j,
		std::size_t	itau
	)

The n-th tau derivative of \(u(\tau)\), the argument of sqrt in the cross aij term

Parameters

tau	The reciprocal reduced temperature \(\tau=T_r/T\)
i	The first index
j	The first index
itau	The number of derivatives of \(a_{ij}\) to take with respect to \(\tau\) (itau=0 is just a_{ij}, itau=1 is d(a_ij)/d(tau), etc.)

Definition at line 320 of file GeneralizedCubic.cpp.

Member Data Documentation

◆ acentric

std::vector<double> AbstractCubic::acentric

protected

Vector of acentric factors (unitless)

Definition at line 116 of file GeneralizedCubic.h.

◆ alpha

std::vector<shared_ptr<AbstractCubicAlphaFunction> > AbstractCubic::alpha

protected

The vector of alpha functions for the pure components

Definition at line 123 of file GeneralizedCubic.h.

◆ cm

double AbstractCubic::cm

protected

The volume translation parameter.

Definition at line 122 of file GeneralizedCubic.h.

◆ Delta_1

double AbstractCubic::Delta_1

protected

The first cubic constant.

Definition at line 118 of file GeneralizedCubic.h.

◆ Delta_2

double AbstractCubic::Delta_2

protected

The second cubic constant.

Definition at line 119 of file GeneralizedCubic.h.

◆ k

std::vector<std::vector<double> > AbstractCubic::k

protected

The interaction parameters (k_ii = 0)

Definition at line 121 of file GeneralizedCubic.h.

◆ m_aii_cache

std::vector<std::array<double, 5> > AbstractCubic::m_aii_cache

mutableprotected

Definition at line 126 of file GeneralizedCubic.h.

◆ m_alpha_versions_cache

std::vector<unsigned long> AbstractCubic::m_alpha_versions_cache

mutableprotected

alpha[i]->version() values recorded when m_aii_cache was last populated; used together with m_tau_cache to detect when an alpha function was mutated (e.g., via set_Tr_over_Tci()) without going through one of AbstractCubic's own cache-invalidating setters.

Definition at line 130 of file GeneralizedCubic.h.

◆ m_b0_ii_cache

std::vector<double> AbstractCubic::m_b0_ii_cache

mutableprotected

Cache: per-component covolumes b0_ii(i). These depend only on Tc, pc and R_u (fixed at construction), so they are computed once on first use; bm_term() reads them instead of re-evaluating the R_u*Tc/pc division on every call.

Definition at line 134 of file GeneralizedCubic.h.

◆ m_tau_cache

double AbstractCubic::m_tau_cache

mutableprotected

Cache: aii_term values for the most recent tau. Populated lazily by _ensure_aii_cache().

Definition at line 125 of file GeneralizedCubic.h.

◆ N

int AbstractCubic::N

protected

Number of components in the mixture.

Definition at line 120 of file GeneralizedCubic.h.

◆ pc

std::vector<double> AbstractCubic::pc

protected

Vector of critical pressures (in Pa)

Definition at line 115 of file GeneralizedCubic.h.

◆ R_u

double AbstractCubic::R_u

protected

The universal gas constant in J/(mol*K)

Definition at line 117 of file GeneralizedCubic.h.

◆ rho_r

double AbstractCubic::rho_r

protected

The reducing density to be used [mol/m3].

Definition at line 112 of file GeneralizedCubic.h.

◆ T_r

double AbstractCubic::T_r

protected

The reducing temperature to be used [K].

Definition at line 113 of file GeneralizedCubic.h.

◆ Tc

std::vector<double> AbstractCubic::Tc

protected

Vector of critical temperatures (in K)

Definition at line 114 of file GeneralizedCubic.h.

The documentation for this class was generated from the following files:

src/Backends/Cubics/GeneralizedCubic.h
src/Backends/Cubics/GeneralizedCubic.cpp

Detailed Description

Public Member Functions

Protected Member Functions

Protected Attributes

Constructor & Destructor Documentation

◆ AbstractCubic()

◆ ~AbstractCubic()

Member Function Documentation

◆ _ensure_aii_cache()

◆ a0_ii()

◆ A_term()

◆ aii_term()

◆ aij_term()

◆ alphar()

◆ am_term()

◆ b0_ii()

◆ bm_term()

◆ c_term()

◆ cm_term()

◆ d2_A_term_dxidxj()

◆ d2_alphar_dxidxj()

◆ d2_am_term_dxidxj()

◆ d2_bm_term_dxidxj()

◆ d2_c_term_dxidxj()

◆ d2_PI_12_dxidxj()

◆ d2_psi_minus_dxidxj()

◆ d2_psi_plus_dxidxj()

◆ d2_tau_times_a_dxidxj()

◆ d3_A_term_dxidxjdxk()

◆ d3_alphar_dxidxjdxk()

◆ d3_am_term_dxidxjdxk()

◆ d3_bm_term_dxidxjdxk()

◆ d3_c_term_dxidxjdxk()

◆ d3_PI_12_dxidxjdxk()

◆ d3_psi_minus_dxidxjdxk()

◆ d3_psi_plus_dxidxjdxk()

◆ d3_tau_times_a_dxidxjdxk()

◆ d_A_term_dxi()

◆ d_alphar_dxi()

◆ d_am_term_dxi()

◆ d_bm_term_dxi()

◆ d_c_term_dxi()

◆ d_PI_12_dxi()

◆ d_psi_minus_dxi()

◆ d_psi_plus_dxi()

◆ d_tau_times_a_dxi()

◆ get_acentric()

◆ get_all_alpha_functions()

◆ get_alpha_function()

◆ get_cm()

◆ get_Delta_1()

◆ get_Delta_2()

◆ get_interaction_parameter()

◆ get_kij()

◆ get_kmat()

◆ get_pc()

◆ get_Q_k()

◆ get_R_u()

◆ get_rhor()

◆ get_Tc()

◆ get_Tr()

◆ m_ii()

◆ PI_12()

◆ psi_minus()

◆ psi_plus()

◆ set_all_alpha_functions()

◆ set_alpha()

◆ set_alpha_function()

◆ set_C_MC()

◆ set_C_Twu()

◆ set_cm()

◆ set_interaction_parameter()

◆ set_kij()

◆ set_kmat()

◆ set_Q_k()

◆ set_rhor()

◆ set_Tr()

◆ tau_times_a()

◆ u_term()

Member Data Documentation