van der Waals equation of state: p = RT/(1/rho - b) - a * rho^2 with a = 27/64 * (R*Tc)^2 / Pc b = 1/8 * (R*Tc) / Pc More...

#include <VanDerWaalsEoS.h>

Inheritance diagram for Nektar::VanDerWaalsEoS:

[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

Protected Attributes inherited from Nektar::EquationOfState
NekDouble	m_gamma

NekDouble	m_gasConstant

NekDouble	m_gammaMone

NekDouble	m_gammaMoneOgasConst

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

	~VanDerWaalsEoS (void) override

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< VanDerWaalsEoS >

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

van der Waals equation of state: p = RT/(1/rho - b) - a * rho^2 with a = 27/64 * (R*Tc)^2 / Pc b = 1/8 * (R*Tc) / Pc

Definition at line 49 of file VanDerWaalsEoS.h.

Constructor & Destructor Documentation

◆ VanDerWaalsEoS()

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

private

Definition at line 47 of file VanDerWaalsEoS.cpp.

    : EquationOfState(pSession)
{
    NekDouble Tcrit, Pcrit;
    pSession->LoadParameter("Tcrit", Tcrit);
    pSession->LoadParameter("Pcrit", Pcrit);
 
    m_a = 27.0 / 64.0 * m_gasConstant * m_gasConstant * Tcrit * Tcrit / Pcrit;
    m_b = 1.0 / 8.0 * m_gasConstant * Tcrit / Pcrit;
}

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

◆ ~VanDerWaalsEoS()

Nektar::VanDerWaalsEoS::~VanDerWaalsEoS ( void )

inlineoverrideprivate

Definition at line 91 of file VanDerWaalsEoS.h.

91{};

Member Function Documentation

◆ create()

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

inlinestatic

Creates an instance of this class.

Definition at line 55 of file VanDerWaalsEoS.h.

    {
        EquationOfStateSharedPtr p =
            MemoryManager<VanDerWaalsEoS>::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<T>::value || tinysimd::is_vector_floating_point<T>::value>::type>

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

inlineprivate

Definition at line 104 of file VanDerWaalsEoS.h.

    {
        return (e + m_a * rho) * (m_gamma - 1) / (1.0 / rho - m_b) -
               m_a * rho * rho;
    }

References m_a, m_b, and Nektar::EquationOfState::m_gamma.

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::VanDerWaalsEoS::GetTemperatureKernel	(	const T &	rho,
		const T &	e
	)

inlineprivate

Definition at line 96 of file VanDerWaalsEoS.h.

    {
        return (e + m_a * rho) * (m_gamma - 1) / m_gasConstant;
    }

References m_a, Nektar::EquationOfState::m_gamma, and Nektar::EquationOfState::m_gasConstant.

Referenced by v_GetTemperature().

◆ v_GetDPDe_rho()

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

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 102 of file VanDerWaalsEoS.cpp.

{
    return (m_gamma - 1) / (1.0 / rho - m_b);
}

References m_b, and Nektar::EquationOfState::m_gamma.

◆ v_GetDPDrho_e()

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

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 90 of file VanDerWaalsEoS.cpp.

{
    NekDouble result;
 
    result = (m_gamma - 1) * (e + 2 * m_a * rho - m_a * m_b * rho * rho);
    result = result / ((1 - m_b * rho) * (1 - m_b * rho));
    result = result - 2 * m_a * rho;
 
    return result;
}

References m_a, m_b, and Nektar::EquationOfState::m_gamma.

◆ v_GetEFromRhoP()

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

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 108 of file VanDerWaalsEoS.cpp.

{
    return (p + m_a * rho * rho) * (1.0 / rho - m_b) / (m_gamma - 1) -
           m_a * rho;
}

References m_a, m_b, Nektar::EquationOfState::m_gamma, and CellMLToNektar.cellml_metadata::p.

◆ v_GetEntropy()

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

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 81 of file VanDerWaalsEoS.cpp.

{
    NekDouble T = GetTemperature(rho, e);
    NekDouble sIg =
        m_gasConstant / (m_gamma - 1) * log(T) - m_gasConstant * log(rho);
 
    return sIg + m_gasConstant * log(1 - m_b * rho);
}

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

◆ v_GetPressure() [1/2]

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

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 70 of file VanDerWaalsEoS.cpp.

{
    return GetPressureKernel(rho, e);
}

References GetPressureKernel().

◆ v_GetPressure() [2/2]

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

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 76 of file VanDerWaalsEoS.cpp.

{
    return GetPressureKernel(rho, e);
}

References GetPressureKernel().

◆ v_GetRhoFromPT()

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

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 115 of file VanDerWaalsEoS.cpp.

{
    // First solve for the compressibility factor Z using the cubic equation
    //    Z^3 + k1 * Z^2 + k2 * Z + k3 = 0
    //    for van der Waals:
    //        k1 = -(B+1), k2 = A,  k3 = -AB
    //    where A = aP/(RT)^2, B = bP/(RT)
    NekDouble A = m_a * p / (m_gasConstant * m_gasConstant * T * T);
    NekDouble B = m_b * p / (m_gasConstant * T);
 
    NekDouble k1 = -(B + 1);
    NekDouble k2 = A;
    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 VanDerWaalsEoS::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(), m_a, m_b, Nektar::EquationOfState::m_gasConstant, and CellMLToNektar.cellml_metadata::p.

◆ v_GetTemperature() [1/2]

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

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 59 of file VanDerWaalsEoS.cpp.

{
    return GetTemperatureKernel(rho, e);
}

References GetTemperatureKernel().

◆ v_GetTemperature() [2/2]

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

finalprotectedvirtual

Implements Nektar::EquationOfState.

Definition at line 65 of file VanDerWaalsEoS.cpp.

{
    return GetTemperatureKernel(rho, e);
}

References GetTemperatureKernel().

Friends And Related Function Documentation

◆ MemoryManager< VanDerWaalsEoS >

friend class MemoryManager< VanDerWaalsEoS >

friend

Definition at line 1 of file VanDerWaalsEoS.h.

Member Data Documentation

◆ className

std::string Nektar::VanDerWaalsEoS::className

static

Initial value:

=
    GetEquationOfStateFactory().RegisterCreatorFunction(
        "VanDerWaals", VanDerWaalsEoS::create,
        "Van der Waals equation of state.")

Name of the class.

Definition at line 64 of file VanDerWaalsEoS.h.

◆ m_a

NekDouble Nektar::VanDerWaalsEoS::m_a

protected

Definition at line 67 of file VanDerWaalsEoS.h.

Referenced by GetPressureKernel(), GetTemperatureKernel(), v_GetDPDrho_e(), v_GetEFromRhoP(), v_GetRhoFromPT(), and VanDerWaalsEoS().

◆ m_b

NekDouble Nektar::VanDerWaalsEoS::m_b

protected

Definition at line 68 of file VanDerWaalsEoS.h.

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

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Private Member Functions

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ VanDerWaalsEoS()

◆ ~VanDerWaalsEoS()

Member Function Documentation

◆ create()

◆ GetPressureKernel()

◆ GetTemperatureKernel()

◆ 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< VanDerWaalsEoS >

Member Data Documentation

◆ className

◆ m_a

◆ m_b