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_