The solution time for a chemically reacting flow problem increases with the size of the reaction mechanism used. Typically, this relationship is
where 
, 
, 
, and 
are constants. However, 
if finite-difference Jacobian is applied.
Dynamic Mechanism Reduction can accelerate the simulation by
decreasing the number of species (
)
and number of reactions (
) in the chemical mechanism. In general, more reduction
results in faster, but less accurate simulations. Mechanism reduction
seeks to decrease the mechanism size while limiting accuracy loss
to some predefined tolerances.
Unlike skeletal reduction where mechanism reduction is completed at the pre-solution stage to create a single reduced mechanism that is used throughout the simulation, Dynamic Mechanism Reduction is performed "on the fly" in every cell (or particle), at every flow iteration (for steady simulations) or time step (for transient simulations). Since the mechanism is only required to be accurate at the local cell conditions, Dynamic Mechanism Reduction can be used with a higher level of reduction yet less accuracy loss than skeletal mechanism [[394], [489]].
Mechanism reduction in Ansys Fluent is performed using the Directed Relation Graph (DRG) approach [[392], [393]], described next.
Given a list of species that need to be modeled accurately (called “targets”), DRG eliminates all species and reactions in the mechanism that do not contribute significantly (directly or indirectly) to predicting the evolution of the targets.
To generate the reduced mechanism, DRG implements the following steps.
DRG considers normalized contribution of each non-target species
to overall production of each target species 
within a single cell:
(7–171)
where 
is a
chemical rate of elementary reaction 
at a local cell condition defined
by the temperature 
, the pressure 
, and the species mass fraction 
is a stoichiometric
coefficient of species 
in reaction 
Species
is retained in the mechanism if and only if the
largest reaction rate involving both species, 
and 
, is larger than a fraction 
of the largest reaction
rate involving species 
within the cell:
(7–172)
where
is a specified error tolerance.Normalized contribution value
is computed for every
non-target species 
in the mechanism, to identify all non-target species
that directly contribute significantly to modeling target species 
. These species constitute
the dependent set of 
. This process is repeated for
all target species, and a comprehensive dependent set is created as
the union of individual dependent sets for all targets.In the next step, DRG algorithm, in a similar manner, identifies indirect contributors, which are species that directly impact the dependent set, rather than the targets. In other words, if species
is included in the comprehensive dependent set created
in step 1, then all the remaining species 
with 
must also be included. The procedure outlined in
step 1 is applied to each species 
in the dependent set to generate
the list of species that contribute to its production or consumption.This process is continued for each species added to the mechanism, until no new species qualifies to be added to the comprehensive dependent set.
The resulting set of species (including the targets) constitutes the species retained in the mechanism. All the other species, that is all the species
for which 
for all species 
included in the resulting set of species, are considered
unimportant and are eliminated from the mechanism.Finally, all reactions that do not involve any of the retained species are also eliminated from the mechanism. The resulting mechanism is the final reduced mechanism.
A lower-dimensional ODE system is solved, involving only the retained species and reactions. The eliminated species mass fractions are stored for computing mixture quantities such as density and heat capacity.
It is important to note that computational expense of the DRG
method has been shown to be linear in the number of reactions 
in the full detailed mechanism. This small
additional overhead is typically significantly outweighed by the acceleration
due to Dynamic Mechanism Reduction using DRG.
Mechanism reduction is controlled by the following two parameters in Ansys Fluent:
Error Tolerance
The default value for error tolerance
is 0.01.Target Species List (adjustable only in expert mode, accessible in the TUI)
The default list of target species consists of 3 constituents. Hydrogen radical is explicitly defined as the first target species. Hydrogen radical is used as a default target species because it is strongly linked to heat release in combustion; accurate prediction of this species should ensure accurate prediction of heat release. Two other species with the largest mass fractions are added to the target species list by DRG algorithm at each time step or flow iteration.
There is also an option to remove a species from the target list whenever its mass fraction is below a given threshold. This option is disabled by default in Ansys Fluent (that is, the default value for minimum mass fraction is 0).
In general, a smaller value of error tolerance 
and a larger value
of number of targets 
yield larger, more accurate mechanisms, but slower
simulations. The default settings should balance accuracy and efficiency
well for most simulations. However, these parameters may require more
careful selection for some problems, such as auto-ignition of highly
complex fuels. For further instructions on how to use Dynamic Mechanism
Reduction, see Using Dynamic Mechanism Reduction in the Fluent User's Guide.