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
virtual NekDouble	v_GetTemperature (const NekDouble &rho, const NekDouble &e) override final

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

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

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

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

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

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

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

virtual NekDouble	v_GetRhoFromPT (const NekDouble &rho, const NekDouble &p) override 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_GetSoundSpeed (const NekDouble &rho, const NekDouble &e)

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)

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

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

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

template<class T , typename = typename std::enable_if< std::is_floating_point<T>::value \|\| tinysimd::is_vector_floating_point<T>::value>::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 ()

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 47 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 )

inlineprivate

Definition at line 106 of file RedlichKwongEoS.h.

106 {};

Member Function Documentation

◆ Alpha()

template<class T , typename = typename std::enable_if< std::is_floating_point<T>::value || tinysimd::is_vector_floating_point<T>::value>::type>

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

inlineprivate

Definition at line 112 of file RedlichKwongEoS.h.

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

References tinysimd::sqrt().

Referenced by 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 CellMLToNektar.cellml_metadata::p.

◆ GetPressureKernel()

template<class T , typename = typename std::enable_if< std::is_floating_point<T>::value || tinysimd::is_vector_floating_point<T>::value>::type>

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

inlineprivate

Definition at line 172 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 CellMLToNektar.cellml_metadata::p.

Referenced by v_GetPressure().

◆ GetTemperatureKernel()

template<class T , typename = typename std::enable_if< std::is_floating_point<T>::value || tinysimd::is_vector_floating_point<T>::value>::type>

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

inlineprivate

Definition at line 129 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(), and tinysimd::sqrt().

Referenced by v_GetTemperature().

◆ LogTerm()

template<class T , typename = typename std::enable_if< std::is_floating_point<T>::value || tinysimd::is_vector_floating_point<T>::value>::type>

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

inlineprivate

Definition at line 121 of file RedlichKwongEoS.h.

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

References tinysimd::log().

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

◆ v_GetDPDe_rho()

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

finaloverrideprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 115 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
	)

finaloverrideprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 95 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
	)

finaloverrideprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 138 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
	)

finaloverrideprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 80 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
	)

finaloverrideprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 69 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
	)

finaloverrideprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 75 of file RedlichKwongEoS.cpp.

 {
     return GetPressureKernel(rho, e);
 }

References GetPressureKernel().

◆ v_GetRhoFromPT()

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

finaloverrideprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 182 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
	)

finaloverrideprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 58 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
	)

finaloverrideprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 64 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 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 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 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