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[Doc] Add detailed descriptions to classes ChebyshevRate and Plog

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The descriptions are essentially taken from the CTI guide (reactions.rst)
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Ray Speth 2016-04-15 12:31:19 -04:00
parent 7124385292
commit fb346d85bc
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include/cantera/kinetics/RxnRates.h
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@ -190,6 +190,22 @@ protected:
//! Pressure-dependent reaction rate expressed by logarithmically interpolating
//! between Arrhenius rate expressions at various pressures.
/*!
* Given two rate expressions at two specific pressures:
*
* * \f$ P_1: k_1(T) = A_1 T^{b_1} e^{E_1 / RT} \f$
* * \f$ P_2: k_2(T) = A_2 T^{b_2} e^{E_2 / RT} \f$
*
* The rate at an intermediate pressure \f$ P_1 < P < P_2 \f$ is computed as
* \f[
* \log k(T,P) = \log k_1(T) + \bigl(\log k_2(T) - \log k_1(T)\bigr)
* \frac{\log P - \log P_1}{\log P_2 - \log P_1}
* \f]
* Multiple rate expressions may be given at the same pressure, in which case
* the rate used in the interpolation formula is the sum of all the rates given
* at that pressure. For pressures outside the given range, the rate expression
* at the nearest pressure is used.
*/
class Plog
{
public:
@ -292,6 +308,33 @@ protected:
//! 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:
* \f[
* \log k(T,P) = \sum_{t=1}^{N_T} \sum_{p=1}^{N_P} \alpha_{tp}
* \phi_t(\tilde{T}) \phi_p(\tilde{P})
* \f]
* where \f$\alpha_{tp}\f$ are the constants defining the rate, \f$\phi_n(x)\f$
* is the Chebyshev polynomial of the first kind of degree *n* evaluated at
* *x*, and
* \f[
* \tilde{T} \equiv \frac{2T^{-1} - T_\mathrm{min}^{-1} - T_\mathrm{max}^{-1}}
* {T_\mathrm{max}^{-1} - T_\mathrm{min}^{-1}}
* \f]
* \f[
* \tilde{P} \equiv \frac{2 \log P - \log P_\mathrm{min} - \log P_\mathrm{max}}
* {\log P_\mathrm{max} - \log P_\mathrm{min}}
* \f]
* are reduced temperature and reduced pressures which map the ranges
* \f$ (T_\mathrm{min}, T_\mathrm{max}) \f$ and
* \f$ (P_\mathrm{min}, P_\mathrm{max}) \f$ to (-1, 1).
*
* A Chebyshev rate expression is specified in terms of the coefficient matrix
* \f$ \alpha \f$ 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.
*/
class ChebyshevRate
{
public: