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Modelisation of combustion equilibria with Monte‐Carlo numerical method
Author(s) -
Brunet L.,
ForichonChaumet N.,
Lombard J. M.,
Espagnacq A.
Publication year - 1997
Publication title -
propellants, explosives, pyrotechnics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.56
H-Index - 65
eISSN - 1521-4087
pISSN - 0721-3115
DOI - 10.1002/prep.19970220602
Subject(s) - monte carlo method , computation , mathematics , constraint (computer aided design) , numerical analysis , combustion , chaotic , lagrange multiplier , quasi monte carlo method , mathematical optimization , monte carlo molecular modeling , computer science , algorithm , mathematical analysis , geometry , chemistry , markov chain monte carlo , statistics , artificial intelligence , organic chemistry
The computation of complex combustions is made classically by using an iterative Newton‐Raphson method, applied to the resolution of a system of equations under constraint by the method of Lagrange multipliers. In many mineral combustions, there are products of reaction that present the same formula but belong to different phases (solids, liquids or gaseous). In these cases, the classic method ends frequently in singular matrix. Indeed, combustion equations can present in these cases, several equal or very close solutions, which induce a numerical fork phenomenon (“stiff” problems) and a chaotic algorithm behaviour. The method presented uses a Monte‐Carlo random algorithm: the Method of Random mass Statements. It presents the advantage of converging in numerically stiff cases. It furthermore provides results equal to the classic method for non‐stiff problems.