Numerical Algorithms for the Parametric Continuation of Stiff ODEs Deriving from the Modeling of Combustion with Detailed Chemical Mechanisms

The use of detailed chemical mechanisms is becoming increasingly necessary during the actual transition of energy production from fossil to renewable fuels. Indeed, the modern renewable fuels are characterized by a composition more complex than traditional fossil fuels due to the variability of the properties of the primary source, i.e. biomass. The parametric continuation can be a formidable tool to study the behavior of these new fuels allowing to promptly assess equilibrium conditions varying the main operative parameters. However, parametric continuation is a very computationally demanding procedure, both for the number of elementary operations needed and for the memory requirements. Actually, only very recently some approaches that allow affording this computation with chemical mechanisms composed of hundreds of chemical species and thousands of reactions have been proposed [1, 2, 37]. Starting from the procedure presented in [1], this paper illustrates further improvements of key steps that usually represents a bottleneck for the effective computation of parametric continuations and for the identification of bifurcation points.