Pressure-dependent rate expression where the rate coefficient is expressed as a bivariate Chebyshev polynomial in temperature and pressure. More...

#include <RxnRates.h>

Public Member Functions
	ChebyshevRate ()
	Default constructor. More...

	ChebyshevRate (double Tmin, double Tmax, double Pmin, double Pmax, const Array2D &coeffs)
	Constructor directly from coefficient array. More...

void	update_C (const doublereal *c)
	Update concentration-dependent parts of the rate coefficient. More...

doublereal	updateRC (doublereal logT, doublereal recipT) const
	Update the value the rate constant. More...

double	Tmin () const
	Minimum valid temperature [K]. More...

double	Tmax () const
	Maximum valid temperature [K]. More...

double	Pmin () const
	Minimum valid pressure [Pa]. More...

double	Pmax () const
	Maximum valid pressure [Pa]. More...

size_t	nPressure () const
	Number of points in the pressure direction. More...

size_t	nTemperature () const
	Number of points in the temperature direction. More...

const vector_fp &	coeffs () const
	Access the Chebyshev coefficients. More...

Static Public Member Functions
static int	type ()
	return the rate coefficient type. More...

Protected Attributes
double	Tmin_

double	Tmax_
	valid temperature range More...

double	Pmin_

double	Pmax_
	valid pressure range More...

double	TrNum_

double	TrDen_
	terms appearing in the reduced temperature More...

double	PrNum_

double	PrDen_
	terms appearing in the reduced pressure More...

size_t	nP_
	number of points in the pressure direction More...

size_t	nT_
	number of points in the temperature direction More...

vector_fp	chebCoeffs_
	Chebyshev coefficients, length nP * nT. More...

vector_fp	dotProd_
	dot product of chebCoeffs with the reduced pressure polynomial More...

Detailed Description

Pressure-dependent rate expression where the rate coefficient is expressed as a bivariate Chebyshev polynomial in temperature and pressure.

The rate constant can be written as:

\[ \log k(T,P) = \sum_{t=1}^{N_T} \sum_{p=1}^{N_P} \alpha_{tp} \phi_t(\tilde{T}) \phi_p(\tilde{P}) \]

where \(\alpha_{tp}\) are the constants defining the rate, \(\phi_n(x)\) is the Chebyshev polynomial of the first kind of degree n evaluated at x, and

\[ \tilde{T} \equiv \frac{2T^{-1} - T_\mathrm{min}^{-1} - T_\mathrm{max}^{-1}} {T_\mathrm{max}^{-1} - T_\mathrm{min}^{-1}} \]

\[ \tilde{P} \equiv \frac{2 \log P - \log P_\mathrm{min} - \log P_\mathrm{max}} {\log P_\mathrm{max} - \log P_\mathrm{min}} \]

are reduced temperature and reduced pressures which map the ranges \( (T_\mathrm{min}, T_\mathrm{max}) \) and \( (P_\mathrm{min}, P_\mathrm{max}) \) to (-1, 1).

A Chebyshev rate expression is specified in terms of the coefficient matrix \( \alpha \) and the temperature and pressure ranges. Note that the Chebyshev polynomials are not defined outside the interval (-1,1), and therefore extrapolation of rates outside the range of temperatures and pressures for which they are defined is strongly discouraged.

Definition at line 355 of file RxnRates.h.

Constructor & Destructor Documentation

◆ ChebyshevRate() [1/2]

ChebyshevRate ( )

inline

Default constructor.

Definition at line 369 of file RxnRates.h.

◆ ChebyshevRate() [2/2]

ChebyshevRate	(	double	Tmin,
		double	Tmax,
		double	Pmin,
		double	Pmax,
		const Array2D &	coeffs
	)

Constructor directly from coefficient array.

Definition at line 133 of file RxnRates.cpp.

References ChebyshevRate::chebCoeffs_, ChebyshevRate::coeffs(), ChebyshevRate::nP_, ChebyshevRate::nT_, ChebyshevRate::Pmax(), ChebyshevRate::Pmin(), ChebyshevRate::PrDen_, ChebyshevRate::Tmax(), ChebyshevRate::Tmin(), and ChebyshevRate::TrDen_.

Member Function Documentation

◆ type()

static int type ( )

inlinestatic

return the rate coefficient type.

Deprecated:: To be removed after Cantera 2.5.

Definition at line 362 of file RxnRates.h.

References Cantera::warn_deprecated().

◆ update_C()

void update_C ( const doublereal * c )

inline

Update concentration-dependent parts of the rate coefficient.

Parameters

c	base-10 logarithm of the pressure in Pa

Definition at line 386 of file RxnRates.h.

References ChebyshevRate::chebCoeffs_, ChebyshevRate::dotProd_, ChebyshevRate::nP_, ChebyshevRate::nT_, and ChebyshevRate::PrDen_.

◆ updateRC()

doublereal updateRC	(	doublereal	logT,
		doublereal	recipT
	)		const

inline

Update the value the rate constant.

This function returns the actual value of the rate constant.

Definition at line 409 of file RxnRates.h.

References ChebyshevRate::dotProd_, ChebyshevRate::nT_, and ChebyshevRate::TrDen_.

◆ Tmin()

double Tmin ( ) const

inline

Minimum valid temperature [K].

Definition at line 425 of file RxnRates.h.

Referenced by ChebyshevRate::ChebyshevRate().

◆ Tmax()

double Tmax ( ) const

inline

Maximum valid temperature [K].

Definition at line 430 of file RxnRates.h.

References ChebyshevRate::Tmax_.

Referenced by ChebyshevRate::ChebyshevRate().

◆ Pmin()

double Pmin ( ) const

inline

Minimum valid pressure [Pa].

Definition at line 435 of file RxnRates.h.

Referenced by ChebyshevRate::ChebyshevRate().

◆ Pmax()

double Pmax ( ) const

inline

Maximum valid pressure [Pa].

Definition at line 440 of file RxnRates.h.

References ChebyshevRate::Pmax_.

Referenced by ChebyshevRate::ChebyshevRate().

◆ nPressure()

size_t nPressure ( ) const

inline

Number of points in the pressure direction.

Definition at line 445 of file RxnRates.h.

References ChebyshevRate::nP_.

◆ nTemperature()

size_t nTemperature ( ) const

inline

Number of points in the temperature direction.

Definition at line 450 of file RxnRates.h.

References ChebyshevRate::nT_.

◆ coeffs()

const vector_fp& coeffs ( ) const

inline

Access the Chebyshev coefficients.

\( \alpha_{t,p} = \mathrm{coeffs}[N_P*t + p] \) where \( 0 <= t < N_T \) and \( 0 <= p < N_P \).

Definition at line 459 of file RxnRates.h.

References ChebyshevRate::chebCoeffs_.

Referenced by ChebyshevRate::ChebyshevRate().

Member Data Documentation

◆ Tmax_

double Tmax_

protected

valid temperature range

Definition at line 464 of file RxnRates.h.

Referenced by ChebyshevRate::Tmax().

◆ Pmax_

double Pmax_

protected

valid pressure range

Definition at line 465 of file RxnRates.h.

Referenced by ChebyshevRate::Pmax().

◆ TrDen_

double TrDen_

protected

terms appearing in the reduced temperature

Definition at line 466 of file RxnRates.h.

Referenced by ChebyshevRate::ChebyshevRate(), and ChebyshevRate::updateRC().

◆ PrDen_

double PrDen_

protected

terms appearing in the reduced pressure

Definition at line 467 of file RxnRates.h.

Referenced by ChebyshevRate::ChebyshevRate(), and ChebyshevRate::update_C().

◆ nP_

size_t nP_

protected

number of points in the pressure direction

Definition at line 469 of file RxnRates.h.

Referenced by ChebyshevRate::ChebyshevRate(), ChebyshevRate::nPressure(), and ChebyshevRate::update_C().

◆ nT_

size_t nT_

protected

number of points in the temperature direction

Definition at line 470 of file RxnRates.h.

Referenced by ChebyshevRate::ChebyshevRate(), ChebyshevRate::nTemperature(), ChebyshevRate::update_C(), and ChebyshevRate::updateRC().

◆ chebCoeffs_

vector_fp chebCoeffs_

protected

Chebyshev coefficients, length nP * nT.

Definition at line 471 of file RxnRates.h.

Referenced by ChebyshevRate::ChebyshevRate(), ChebyshevRate::coeffs(), and ChebyshevRate::update_C().

◆ dotProd_

vector_fp dotProd_

protected

dot product of chebCoeffs with the reduced pressure polynomial

Definition at line 472 of file RxnRates.h.

Referenced by ChebyshevRate::update_C(), and ChebyshevRate::updateRC().

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

Public Member Functions

Static Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ ChebyshevRate() [1/2]

◆ ChebyshevRate() [2/2]

Member Function Documentation

◆ type()

◆ update_C()

◆ updateRC()

◆ Tmin()

◆ Tmax()

◆ Pmin()

◆ Pmax()

◆ nPressure()

◆ nTemperature()

◆ coeffs()

Member Data Documentation

◆ Tmax_

◆ Pmax_

◆ TrDen_

◆ PrDen_

◆ nP_

◆ nT_

◆ chebCoeffs_

◆ dotProd_