Directed Relation Graph with Error Propagation (DRGEP) - Revision history

Seltz at 20:48, 26 March 2017

2017-03-26T20:48:22Z

Seltz at 20:21, 26 March 2017

2017-03-26T20:21:55Z

Seltz at 18:58, 26 March 2017

2017-03-26T18:58:12Z

Seltz: Created page with "DRGEP (Directed Relation Graph with Error Propagation) is a method which rank the impact of the species and reactions on the species targeted The DRGEP repertory contains two..."

2017-03-26T17:01:49Z

Created page with "DRGEP (Directed Relation Graph with Error Propagation) is a method which rank the impact of the species and reactions on the species targeted The DRGEP repertory contains two..."

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DRGEP (Directed Relation Graph with Error Propagation) is a method which rank the impact of the species and reactions on the species targeted

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 r_AB and the indirect one r_AD

* 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

@@ Line 1: / Line 1: @@
-The DRGEP (Directed Relation Graph with Error Propagation) method calculates the contribution of all species and reactions on the production rate of the targeted species. First, the rate of direct inter-relation between a target species A and a species B is calculated :
+The DRGEP (Directed Relation Graph with Error Propagation<ref name="wazaa"> T. Lu and C. K. Law. A directed relation graph method for mechanism reduction. Proceedings of the Combustion Institute, 30(1):1333–1341, 2005</ref>) method calculates the contribution of all species and reactions on the production rate of the targeted species. We present here a modified method<ref> N. Jaouen. An automated approach to derive and optimise reduced chemical mechanisms for turbulent combustion</ref> from the original one<ref name="wazaa"/>. First, the influence of a species B on the consumption/production of a target species A is calculated :
 <math> 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|} </math>
@@ Line 14: / Line 14: @@
   </math>
-and <math>\dot{Q}_j</math> the rate of reaction j. Once the direct rate is calculated, the indirect impact of a species D on A is also considered :
+and <math>\dot{Q}_j</math> the rate of reaction j. Next, the indirect impact of a species D on A is also considered :
-<math> r_{AD} =  </math>
+<math> r_{A-D} = max(r_{A-B} \quad \text{x} \quad r_{B-D}, r_{A-D})</math>
 The DRGEP repertory contains two files :
@@ Line 30: / Line 32: @@
 * drgep_species :
-Calculates the rate of direct inter-relation between species r_AB and the indirect one r_AD
+Calculates the rate of direct inter-relation between species <math> r_{A-B} </math> and the indirect one <math> r_{A-D}</math>
 * drgep_reaction :
@@ Line 46: / Line 48: @@
 * drgep_1D_reactions :
 Runs the analysis of drgep_reaction for 1D premix regime

@@ Line 1: / Line 1: @@
-The DRGEP (Directed Relation Graph with Error Propagation) method calculates the contribution of all species and reactions on the production rate of the targeted species. First, the rate of direct inter-relation between two species A and B is calculated :
+The DRGEP (Directed Relation Graph with Error Propagation) method calculates the contribution of all species and reactions on the production rate of the targeted species. First, the rate of direct inter-relation between a target species A and a species B is calculated :
 <math> 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|} </math>
-Then the indirect rate of a species D on A :
+with :
 <math> r_{AD} =  </math>

← Older revision		Revision as of 18:58, 26 March 2017
Line 1:		Line 1:
−	DRGEP (Directed Relation Graph with Error Propagation) ~~is a~~ method ~~which rank~~ the ~~impact~~ of ~~the~~ species and reactions on the ~~species~~ targeted	+	The DRGEP (Directed Relation Graph with Error Propagation) method calculates the contribution of all species and reactions on the production rate of the targeted species. First, the rate of direct inter-relation between two species A and B is calculated :
		+
		+	<math> 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\|} </math>
		+
		+	Then the indirect rate of a species D on A :
		+
		+	<math> r_{AD} = </math>
		+
		+

	The DRGEP repertory contains two files :		The DRGEP repertory contains two files :