When running an Internal Combustion Engine simulation with multiple subsequent cycles, the combustion products will become the residual material in the following cycle. Therefore, the ‘new’ products must be transformed into residual material. This is achieved by reinitializing fuel tracer and reaction progress at specified times:

(7–91)

and

(7–92)

In case of the weighted reaction progress model, the second assignment is equivalent to:

(7–93)

In the expression for the new fuel tracer after reinitialization, , the first term accounts for the excess fuel in the burnt fraction of the mixture, and the second term accounts for the fuel in the fresh fraction.

Note that in the limit of zero scalar dissipation rate, , the reinitialization leaves the component mass fractions effectively unchanged.