# Directed Relation Graph with Error Propagation (DRGEP)

The DRGEP (Directed Relation Graph with Error Propagation[1]) method calculates the contribution of all species and reactions on the production rate of the targeted species. We present here a modified method[2] from the original one[1]. First, the influence of a species B on the consumption/production of a target species A is calculated :

${\displaystyle r_{A-B}={\frac {\sum _{j=1}^{N_{r}}|\nu _{Aj}{\dot {Q}}_{j}\delta _{B_{j}}|}{\sum _{j=1}^{N_{r}}|\nu _{Aj}{\dot {Q}}_{j}|}}}$

with :

${\displaystyle \left\{{\begin{array}{l}\delta _{B_{j}}=1\quad {\text{if B is involved in the jth reaction}}\\\delta _{B_{j}}=0\quad {\text{otherwise}}\end{array}}\right.}$

and ${\displaystyle {\dot {Q}}_{j}}$ the rate of reaction j. Next, the indirect impact of a species D on A is also considered :

${\displaystyle r_{A-D}=max(r_{A-B}\quad {\text{x}}\quad r_{B-D},r_{A-D})}$

The DRGEP repertory contains two files :

- drgep.cpp

- drgep.h

where the DRGEP analysis of species and reactions is defined through the following functions :

• drgep_species :

Calculates the rate of direct inter-relation between species ${\displaystyle r_{A-B}}$ and the indirect one ${\displaystyle r_{A-D}}$

• drgep_reaction :

Calculates the impact of each reaction on the creation and destruction of the target species

• drgep_0D_species :

Runs the analysis of drgep_species for 0D auto-ignition or multiple inlet regime

• drgep_0D_reactions :

Runs the analysis of drgep_reaction for 0D auto-ignition or multiple inlet regime

• drgep_1D_species :

Runs the analysis of drgep_species for 1D premix regime

• drgep_1D_reactions :

Runs the analysis of drgep_reaction for 1D premix regime

### Bibliography

1. T. Lu and C. K. Law. A directed relation graph method for mechanism reduction. Proceedings of the Combustion Institute, 30(1):1333–1341, 2005
2. N. Jaouen. An automated approach to derive and optimise reduced chemical mechanisms for turbulent combustion