where the notation \(t-1\) indicates the variable value in the previous timestep, \(\beta \) is a modified burning rate constant calculated as \(\beta = \beta^{0}\left(1 + 0.276Re^{1/2}Sc^{1/3}\right)\), \(\beta^0\) is an empirically-derived burning rate constant (\(\beta^0\)= 4.8E10-7s-1) from the data of \citealt{tarifa1965}, and \(Sc\) is the Schmidt number (assumed to be 0.7 for air; \citealt{bhutia2010comparison}).
As in \citealt{tse1998flight}, we calculate the Reynolds number Re using the particle information