Redlich-Kwong equation of state: p = RT/(1/rho - b) - a/( sqrt(T / Tc) * (1/rho^2 + b/rho) with a = 0.42748 * (R*Tc)^2 / Pc b = 0.08664 * (R*Tc) / Pc. More...

#include <RedlichKwongEoS.h>

Inheritance diagram for Nektar::RedlichKwongEoS:

[legend]

Static Public Member Functions
static EquationOfStateSharedPtr	create (const LibUtilities::SessionReaderSharedPtr &pSession)
	Creates an instance of this class. More...

Static Public Attributes
static std::string	className
	Name of the class. More...

Protected Member Functions
NekDouble	v_GetTemperature (const NekDouble &rho, const NekDouble &e) final

vec_t	v_GetTemperature (const vec_t &rho, const vec_t &e) final

NekDouble	v_GetPressure (const NekDouble &rho, const NekDouble &e) final

vec_t	v_GetPressure (const vec_t &rho, const vec_t &e) final

NekDouble	v_GetEntropy (const NekDouble &rho, const NekDouble &e) final

NekDouble	v_GetDPDrho_e (const NekDouble &rho, const NekDouble &e) final

NekDouble	v_GetDPDe_rho (const NekDouble &rho, const NekDouble &e) final

NekDouble	v_GetEFromRhoP (const NekDouble &rho, const NekDouble &p) final

NekDouble	v_GetRhoFromPT (const NekDouble &rho, const NekDouble &p) final

Protected Member Functions inherited from Nektar::EquationOfState
	EquationOfState (const LibUtilities::SessionReaderSharedPtr &pSession)
	Constructor. More...

	EquationOfState (const NekDouble &gamma, const NekDouble &gasConstant)
	Programmatic Constructor. More...

virtual NekDouble	v_GetTemperature (const NekDouble &rho, const NekDouble &e)=0

virtual vec_t	v_GetTemperature (const vec_t &rho, const vec_t &e)=0

virtual NekDouble	v_GetPressure (const NekDouble &rho, const NekDouble &e)=0

virtual vec_t	v_GetPressure (const vec_t &rho, const vec_t &e)=0

virtual NekDouble	v_GetSoundSpeed (const NekDouble &rho, const NekDouble &e)

virtual NekDouble	v_GetEntropy (const NekDouble &rho, const NekDouble &e)=0

virtual NekDouble	v_GetDPDrho_e (const NekDouble &rho, const NekDouble &e)=0

virtual NekDouble	v_GetDPDe_rho (const NekDouble &rho, const NekDouble &e)=0

virtual NekDouble	v_GetEFromRhoP (const NekDouble &rho, const NekDouble &p)=0

virtual NekDouble	v_GetRhoFromPT (const NekDouble &rho, const NekDouble &p)=0

Protected Attributes
NekDouble	m_a

NekDouble	m_b

NekDouble	m_Tc

NekDouble	m_Pc

Protected Attributes inherited from Nektar::EquationOfState
NekDouble	m_gamma

NekDouble	m_gasConstant

NekDouble	m_gammaMone

NekDouble	m_gammaMoneOgasConst

Private Member Functions
	RedlichKwongEoS (const LibUtilities::SessionReaderSharedPtr &pSession)

	~RedlichKwongEoS (void) override=default

template<class T , typename = typename std::enable_if< std::is_floating_point_v<T> \|\| tinysimd::is_vector_floating_point_v<T>>::type>
T	Alpha (const T &temp)

template<class T , typename = typename std::enable_if< std::is_floating_point_v<T> \|\| tinysimd::is_vector_floating_point_v<T>>::type>
T	LogTerm (const T &rho)

template<class T , typename = typename std::enable_if< std::is_floating_point_v<T> \|\| tinysimd::is_vector_floating_point_v<T>>::type>
T	GetTemperatureKernel (const T &rho, const T &e)

template<class T , typename = typename std::enable_if< std::is_floating_point_v<T> \|\| tinysimd::is_vector_floating_point_v<T>>::type>
T	GetPressureKernel (const T &rho, const T &e)

Friends
class	MemoryManager< RedlichKwongEoS >

Additional Inherited Members
Public Member Functions inherited from Nektar::EquationOfState
virtual	~EquationOfState ()=default

NekDouble	GetTemperature (const NekDouble &rho, const NekDouble &e)
	Calculate the temperature. More...

vec_t	GetTemperature (const vec_t &rho, const vec_t &e)

NekDouble	GetPressure (const NekDouble &rho, const NekDouble &e)
	Calculate the pressure. More...

vec_t	GetPressure (const vec_t &rho, const vec_t &e)

NekDouble	GetSoundSpeed (const NekDouble &rho, const NekDouble &e)
	Calculate the sound speed. More...

NekDouble	GetEntropy (const NekDouble &rho, const NekDouble &e)
	Calculate the entropy. More...

NekDouble	GetDPDrho_e (const NekDouble &rho, const NekDouble &e)
	Calculate the partial derivative of P(rho,e) with respect to rho. More...

NekDouble	GetDPDe_rho (const NekDouble &rho, const NekDouble &e)
	Calculate the partial derivative of P(rho,e) with respect to e. More...

NekDouble	GetEFromRhoP (const NekDouble &rho, const NekDouble &p)
	Obtain the internal energy from rho and P. More...

NekDouble	GetRhoFromPT (const NekDouble &p, const NekDouble &T)
	Obtain the density from P and T. More...

Detailed Description

Redlich-Kwong equation of state: p = RT/(1/rho - b) - a/( sqrt(T / Tc) * (1/rho^2 + b/rho) with a = 0.42748 * (R*Tc)^2 / Pc b = 0.08664 * (R*Tc) / Pc.

Definition at line 53 of file RedlichKwongEoS.h.

Constructor & Destructor Documentation

◆ RedlichKwongEoS()

Nektar::RedlichKwongEoS::RedlichKwongEoS ( const LibUtilities::SessionReaderSharedPtr & pSession )

private

Definition at line 45 of file RedlichKwongEoS.cpp.

    : EquationOfState(pSession)
{
    pSession->LoadParameter("Tcrit", m_Tc);
    pSession->LoadParameter("Pcrit", m_Pc);
 
    m_a = 0.42748 * m_gasConstant * m_gasConstant * m_Tc * m_Tc / m_Pc;
    m_b = 0.08664 * m_gasConstant * m_Tc / m_Pc;
}

References m_a, m_b, Nektar::EquationOfState::m_gasConstant, m_Pc, and m_Tc.

◆ ~RedlichKwongEoS()

Nektar::RedlichKwongEoS::~RedlichKwongEoS ( void )

overrideprivatedefault

Member Function Documentation

◆ Alpha()

template<class T , typename = typename std::enable_if< std::is_floating_point_v<T> || tinysimd::is_vector_floating_point_v<T>>::type>

T Nektar::RedlichKwongEoS::Alpha ( const T & temp )

inlineprivate

Definition at line 103 of file RedlichKwongEoS.h.

    {
        return 1.0 / sqrt(temp / m_Tc);
    }

References m_Tc, and tinysimd::sqrt().

Referenced by GetPressureKernel(), v_GetDPDe_rho(), v_GetDPDrho_e(), v_GetEFromRhoP(), v_GetEntropy(), and v_GetRhoFromPT().

◆ create()

static EquationOfStateSharedPtr Nektar::RedlichKwongEoS::create ( const LibUtilities::SessionReaderSharedPtr & pSession )

inlinestatic

Creates an instance of this class.

Definition at line 59 of file RedlichKwongEoS.h.

    {
        EquationOfStateSharedPtr p =
            MemoryManager<RedlichKwongEoS>::AllocateSharedPtr(pSession);
        return p;
    }

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), and CellMLToNektar.cellml_metadata::p.

◆ GetPressureKernel()

template<class T , typename = typename std::enable_if< std::is_floating_point_v<T> || tinysimd::is_vector_floating_point_v<T>>::type>

T Nektar::RedlichKwongEoS::GetPressureKernel	(	const T &	rho,
		const T &	e
	)

inlineprivate

Definition at line 163 of file RedlichKwongEoS.h.

    {
        T temp    = GetTemperatureKernel(rho, e);
        T oneOrho = 1.0 / rho;
        T p       = m_gasConstant * temp / (oneOrho - m_b) -
              m_a * Alpha(temp) / (oneOrho * (oneOrho + m_b));
        return p;
    }

References Alpha(), GetTemperatureKernel(), m_a, m_b, Nektar::EquationOfState::m_gasConstant, and CellMLToNektar.cellml_metadata::p.

Referenced by v_GetPressure().

◆ GetTemperatureKernel()

template<class T , typename = typename std::enable_if< std::is_floating_point_v<T> || tinysimd::is_vector_floating_point_v<T>>::type>

T Nektar::RedlichKwongEoS::GetTemperatureKernel	(	const T &	rho,
		const T &	e
	)

inlineprivate

Definition at line 120 of file RedlichKwongEoS.h.

    {
        // First we need to evaluate the log term
        //    ln[1 + b*rho]
        T logTerm = LogTerm(rho);
 
        // The temperature can be expressed as an equation in the form
        //      (T^1/2)^3 + A* T^1/2 + B = 0, which we solve iteratively
        T A = e * (1.0 - m_gamma) / m_gasConstant;
        T B = -3.0 * m_a / (2.0 * m_b * m_gasConstant) * (m_gamma - 1) *
              sqrt(m_Tc) * logTerm;
 
        // Use ideal gas solution as starting guess for iteration
        T sqrtT = sqrt(e * (m_gamma - 1) / m_gasConstant);
        // Newton-Raphson iteration to find T^(1/2)
        T tol                = 1e-6;
        T residual           = 1;
        unsigned int maxIter = 100;
        unsigned int cnt     = 0;
        while (abs(residual) > tol && cnt < maxIter)
        {
            T f      = sqrtT * sqrtT * sqrtT + A * sqrtT + B;
            T df     = 3 * sqrtT * sqrtT + A;
            residual = f / df;
            sqrtT -= residual;
            ++cnt;
        }
        if (cnt == maxIter)
        {
            std::cout << "Newton-Raphson in RedlichKwongEoS::v_GetTemperature "
                         "did not "
                         "converge in "
                      << maxIter << " iterations (residual = " << residual
                      << ")" << std::endl;
        }
 
        // Calculate the temperature
        return sqrtT * sqrtT;
    }

References tinysimd::abs(), LogTerm(), m_a, m_b, Nektar::EquationOfState::m_gamma, Nektar::EquationOfState::m_gasConstant, m_Tc, and tinysimd::sqrt().

Referenced by GetPressureKernel(), and v_GetTemperature().

◆ LogTerm()

template<class T , typename = typename std::enable_if< std::is_floating_point_v<T> || tinysimd::is_vector_floating_point_v<T>>::type>

T Nektar::RedlichKwongEoS::LogTerm ( const T & rho )

inlineprivate

Definition at line 112 of file RedlichKwongEoS.h.

    {
        return log(1.0 + m_b * rho);
    }

References tinysimd::log(), and m_b.

Referenced by GetTemperatureKernel(), v_GetDPDe_rho(), v_GetEFromRhoP(), and v_GetEntropy().

◆ v_GetDPDe_rho()

NekDouble Nektar::RedlichKwongEoS::v_GetDPDe_rho	(	const NekDouble &	rho,
		const NekDouble &	e
	)

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 113 of file RedlichKwongEoS.cpp.

{
    NekDouble T       = GetTemperature(rho, e);
    NekDouble alpha   = Alpha(T);
    NekDouble logTerm = LogTerm(rho);
 
    // First calculate the denominator 1/rho^2 + 2*b/rho - b^2
    //    and sqrt(Alpha) = 1+f_w*(1-sqrt(Tr))
    NekDouble denom = 1.0 / (rho * rho) + m_b / rho;
 
    // Compute cv = dedT_rho
    NekDouble cv = m_gasConstant / (m_gamma - 1) +
                   3 * m_a * alpha * logTerm / (4 * m_b * T);
 
    // Now we obtain dPdT_rho
    NekDouble dPdT =
        m_gasConstant / (1.0 / rho - m_b) + m_a * alpha / (denom * 2 * T);
 
    // The result is dPde_rho = dPdT_rho / cv
    return dPdT / cv;
}

References Alpha(), Nektar::EquationOfState::GetTemperature(), LogTerm(), m_a, m_b, Nektar::EquationOfState::m_gamma, and Nektar::EquationOfState::m_gasConstant.

◆ v_GetDPDrho_e()

NekDouble Nektar::RedlichKwongEoS::v_GetDPDrho_e	(	const NekDouble &	rho,
		const NekDouble &	e
	)

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 93 of file RedlichKwongEoS.cpp.

{
    NekDouble T     = GetTemperature(rho, e);
    NekDouble alpha = Alpha(T);
    NekDouble dPde  = GetDPDe_rho(rho, e);
 
    // Calculate dPdrho_T
    NekDouble dPdrho_T =
        m_gasConstant * T / ((1.0 - m_b * rho) * (1.0 - m_b * rho)) -
        m_a * alpha * rho * (m_b * rho + 2) /
            ((1 + m_b * rho) * (1 + m_b * rho));
 
    // Calculate dedrho_T
    NekDouble dedrho_T = -3 * m_a * alpha / (2 * (1 + m_b * rho));
 
    // The result is dPdrho_e = dPdrho_T - dPde_rho * dedrho_T
    return dPdrho_T - dPde * dedrho_T;
}

References Alpha(), Nektar::EquationOfState::GetDPDe_rho(), Nektar::EquationOfState::GetTemperature(), m_a, m_b, and Nektar::EquationOfState::m_gasConstant.

◆ v_GetEFromRhoP()

NekDouble Nektar::RedlichKwongEoS::v_GetEFromRhoP	(	const NekDouble &	rho,
		const NekDouble &	p
	)

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 136 of file RedlichKwongEoS.cpp.

{
    NekDouble logTerm = LogTerm(rho);
    // First calculate the temperature, which can be expressed as
    //      (T^1/2)^3 + A* T^1/2 + B = 0
    NekDouble A, B;
 
    A = -p * (1.0 / rho - m_b) / m_gasConstant;
    B = -m_a * sqrt(m_Tc) * (1.0 / rho - m_b) /
        (1.0 / (rho * rho) + m_b / rho) / m_gasConstant;
 
    // Use ideal gas solution as starting guess for iteration
    NekDouble sqrtT = sqrt(p / (rho * (m_gamma - 1)));
    // Newton-Raphson iteration to find T^(1/2)
    NekDouble tol      = 1e-6;
    NekDouble maxIter  = 100;
    NekDouble residual = 1;
    NekDouble f, df;
    unsigned int cnt = 0;
    while (abs(residual) > tol && cnt < maxIter)
    {
        f        = sqrtT * sqrtT * sqrtT + A * sqrtT + B;
        df       = 3 * sqrtT * sqrtT + A;
        residual = f / df;
        sqrtT -= residual;
        ++cnt;
    }
    if (cnt == maxIter)
    {
        cout << "Newton-Raphson in RedlichKwongEoS::v_GetEFromRhoP did not "
                "converge in "
             << maxIter << " iterations (residual = " << residual << ")"
             << endl;
    }
 
    // Calculate T
    NekDouble T = sqrtT * sqrtT;
 
    // Calculate internal energy
    return m_gasConstant * T / (m_gamma - 1) -
           3 * m_a * Alpha(T) / (2 * m_b) * logTerm;
}

References tinysimd::abs(), Alpha(), LogTerm(), m_a, m_b, Nektar::EquationOfState::m_gamma, Nektar::EquationOfState::m_gasConstant, m_Tc, CellMLToNektar.cellml_metadata::p, and tinysimd::sqrt().

◆ v_GetEntropy()

NekDouble Nektar::RedlichKwongEoS::v_GetEntropy	(	const NekDouble &	rho,
		const NekDouble &	e
	)

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 78 of file RedlichKwongEoS.cpp.

{
    NekDouble T       = GetTemperature(rho, e);
    NekDouble logTerm = LogTerm(rho);
    // Entropy for an ideal gas
    NekDouble sIg =
        m_gasConstant / (m_gamma - 1) * log(T) - m_gasConstant * log(rho);
 
    NekDouble deltaS = m_gasConstant * log(1 - m_b * rho);
    deltaS -= m_a * Alpha(T) * logTerm / (2 * m_b * T);
 
    return sIg + deltaS;
}

References Alpha(), Nektar::EquationOfState::GetTemperature(), tinysimd::log(), LogTerm(), m_a, m_b, Nektar::EquationOfState::m_gamma, and Nektar::EquationOfState::m_gasConstant.

◆ v_GetPressure() [1/2]

NekDouble Nektar::RedlichKwongEoS::v_GetPressure	(	const NekDouble &	rho,
		const NekDouble &	e
	)

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 67 of file RedlichKwongEoS.cpp.

{
    return GetPressureKernel(rho, e);
}

References GetPressureKernel().

◆ v_GetPressure() [2/2]

vec_t Nektar::RedlichKwongEoS::v_GetPressure	(	const vec_t &	rho,
		const vec_t &	e
	)

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 73 of file RedlichKwongEoS.cpp.

{
    return GetPressureKernel(rho, e);
}

References GetPressureKernel().

◆ v_GetRhoFromPT()

NekDouble Nektar::RedlichKwongEoS::v_GetRhoFromPT	(	const NekDouble &	rho,
		const NekDouble &	p
	)

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 180 of file RedlichKwongEoS.cpp.

{
    // First solve for the compressibility factor Z using the cubic equation
    //    Z^3 + k1 * Z^2 + k2 * Z + k3 = 0
    //    for RedlichKwong:
    //        k1 = -1.0, k2 = A - B - B^2,  k3 = -AB
    //    where A = a*alpha(T)*P/(RT)^2, B = bP/(RT)
    NekDouble A = m_a * Alpha(T) * p / (m_gasConstant * m_gasConstant * T * T);
    NekDouble B = m_b * p / (m_gasConstant * T);
 
    NekDouble k1 = -1.0;
    NekDouble k2 = A - B - B * B;
    NekDouble k3 = -A * B;
 
    // Use ideal gas (Z=1) as starting guess for iteration
    NekDouble Z = 1.0;
    // Newton-Raphson iteration to find Z
    NekDouble tol      = 1e-6;
    NekDouble maxIter  = 100;
    NekDouble residual = 1;
    NekDouble f, df;
    unsigned int cnt = 0;
    while (abs(residual) > tol && cnt < maxIter)
    {
        f        = Z * Z * Z + k1 * Z * Z + k2 * Z + k3;
        df       = 3 * Z * Z + 2 * k1 * Z + k2;
        residual = f / df;
        Z -= residual;
        ++cnt;
    }
    if (cnt == maxIter)
    {
        cout << "Newton-Raphson in RedlichKwongEoS::v_GetRhoFromPT did not "
                "converge in "
             << maxIter << " iterations (residual = " << residual << ")"
             << endl;
    }
 
    // Now calculate rho = p/(ZRT)
    return p / (Z * m_gasConstant * T);
}

References tinysimd::abs(), Alpha(), m_a, m_b, Nektar::EquationOfState::m_gasConstant, and CellMLToNektar.cellml_metadata::p.

◆ v_GetTemperature() [1/2]

NekDouble Nektar::RedlichKwongEoS::v_GetTemperature	(	const NekDouble &	rho,
		const NekDouble &	e
	)

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 56 of file RedlichKwongEoS.cpp.

{
    return GetTemperatureKernel(rho, e);
}

References GetTemperatureKernel().

◆ v_GetTemperature() [2/2]

vec_t Nektar::RedlichKwongEoS::v_GetTemperature	(	const vec_t &	rho,
		const vec_t &	e
	)

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 62 of file RedlichKwongEoS.cpp.

{
    return GetTemperatureKernel(rho, e);
}

References GetTemperatureKernel().

Friends And Related Function Documentation

◆ MemoryManager< RedlichKwongEoS >

friend class MemoryManager< RedlichKwongEoS >

friend

Definition at line 1 of file RedlichKwongEoS.h.

Member Data Documentation

◆ className

std::string Nektar::RedlichKwongEoS::className

static

Initial value:

=
    GetEquationOfStateFactory().RegisterCreatorFunction(
        "RedlichKwong", RedlichKwongEoS::create,
        "Redlich-Kwong equation of state.")

Name of the class.

Definition at line 68 of file RedlichKwongEoS.h.

◆ m_a

NekDouble Nektar::RedlichKwongEoS::m_a

protected

Definition at line 71 of file RedlichKwongEoS.h.

Referenced by GetPressureKernel(), GetTemperatureKernel(), RedlichKwongEoS(), v_GetDPDe_rho(), v_GetDPDrho_e(), v_GetEFromRhoP(), v_GetEntropy(), and v_GetRhoFromPT().

◆ m_b

NekDouble Nektar::RedlichKwongEoS::m_b

protected

Definition at line 72 of file RedlichKwongEoS.h.

Referenced by GetPressureKernel(), GetTemperatureKernel(), LogTerm(), RedlichKwongEoS(), v_GetDPDe_rho(), v_GetDPDrho_e(), v_GetEFromRhoP(), v_GetEntropy(), and v_GetRhoFromPT().

◆ m_Pc

NekDouble Nektar::RedlichKwongEoS::m_Pc

protected

Definition at line 74 of file RedlichKwongEoS.h.

Referenced by RedlichKwongEoS().

◆ m_Tc

NekDouble Nektar::RedlichKwongEoS::m_Tc

protected

Definition at line 73 of file RedlichKwongEoS.h.

Referenced by Alpha(), GetTemperatureKernel(), RedlichKwongEoS(), and v_GetEFromRhoP().

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Private Member Functions

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ RedlichKwongEoS()

◆ ~RedlichKwongEoS()

Member Function Documentation

◆ Alpha()

◆ create()

◆ GetPressureKernel()

◆ GetTemperatureKernel()

◆ LogTerm()

◆ v_GetDPDe_rho()

◆ v_GetDPDrho_e()

◆ v_GetEFromRhoP()

◆ v_GetEntropy()

◆ v_GetPressure() [1/2]

◆ v_GetPressure() [2/2]

◆ v_GetRhoFromPT()

◆ v_GetTemperature() [1/2]

◆ v_GetTemperature() [2/2]

Friends And Related Function Documentation

◆ MemoryManager< RedlichKwongEoS >

Member Data Documentation

◆ className

◆ m_a

◆ m_b

◆ m_Pc

◆ m_Tc