Cantera's implementation of element potential method for solving for equilibrium

[Nick Wogan]

I'm trying to understand Cantera's implementation of the element potential method for solving for chemical equilibrium

The part of Cantera's approach I do not understand very well are the "BasisOptimize" and "ElemRearrange" that are called within the initial estimation of the element potentials (i.e. the Lagrange multipliers). See this link

https://github.com/Cantera/cantera/blob/main/src/equil/BasisOptimize.cpp

My rough understanding is that these routines are necessary to avoid poorly conditioned matrices later on. In the header file (link) BasisOptimize is described as

"""

//! Choose the optimum basis of species for the equilibrium calculations.
/*!
 * This is done by choosing the species with the largest mole fraction not
 * currently a linear combination of the previous components. Then, calculate
 * the stoichiometric coefficient matrix for that basis.

"""

Why is this necessary?

I was wondering if this approach is described in an article or documentation somewhere that is easier to understand than the code. 

Thanks,
Nick

[Shepherd, Joseph E.]

Nick,

The element potential implementation by Reynolds was the basis of the original Cantera algorithm (others will have to speak to what changes have been made I in the past two decades). I have linked Reynolds original reports to my thermo webpage https://shepherd.caltech.edu/EDL/PublicResources/sdt/thermo.html - these discuss the issues around choosing a basis set and preconditioning.

JES

-----Original Message-----
From: canter...@googlegroups.com <canter...@googlegroups.com> On Behalf Of Nick Wogan
Sent: Friday, December 10, 2021 2:46 PM
To: Cantera Users' Group <canter...@googlegroups.com>
Subject: [cantera-users] Cantera's implementation of element potential method for solving for equilibrium

I'm trying to understand Cantera's implementation of the element potential method for solving for chemical equilibrium

The part of Cantera's approach I do not understand very well are the "BasisOptimize" and "ElemRearrange" that are called within the initial estimation of the element potentials (i.e. the Lagrange multipliers). See this link

https://github.com/Cantera/cantera/blob/main/src/equil/BasisOptimize.cpp

My rough understanding is that these routines are necessary to avoid poorly conditioned matrices later on. In the header file (lin <https://github.com/Cantera/cantera/blob/208a89c16aabbe98bbc4de8da66a67b677ff0dbb/include/cantera/equil/MultiPhase.h#L673> k) BasisOptimize is described as

"""
//! Choose the optimum basis of species for the equilibrium calculations.
/*!
* This is done by choosing the species with the largest mole fraction not
* currently a linear combination of the previous components. Then, calculate
* the stoichiometric coefficient matrix for that basis.

"""

Why is this necessary?

I was wondering if this approach is described in an article or documentation somewhere that is easier to understand than the code.

Thanks,
Nick

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