The computational feasibility of many systems with large degrees of freedom such as chemically reacting systems hinges on the reduction of the set to a manageable size with a minimal loss of relevant information. Several sophisticated reduction techniques based on different rationales have been proposed; however, there is no consensus on the best approach or method. While the search for simple but accurate schemes continues, the classical quasi-steady state assumption (QSSA), despite serious shortcomings, remains popular due to its conceptual and computational simplicity. Invoking the similarity between a reduced invariant manifold and a streamline in fluid flow, we develop an advanced QSSA procedure which yields the accuracy of more complex reduction schemes. This flow-physics inspired approach also serves to reconcile the classical QSSA approach with recent methods such as functional equation truncation (FET) and intrinsic low dimensional manifold (ILDM) approaches.

References

References
1.
Peeters
,
N.
, and
Rogg
,
B.
, eds.,
1993
,
Reduced Kinetic Mechanisms for Applications in Combustion Systems
,
Springer-Verlag
,
New York
.
2.
Smooke
,
M.
, ed.,
1992
,
Reduced Kinetic Mechanisms and Flames
,
Springer-Verlag
,
Berlin
.
3.
Maas
,
U.
, and
Pope
,
S. B.
,
1992
, “
Simplifying Chemical Kinetics: Intrinsic Low-Dimensional Manifolds in Composition Space
,”
Combust. Flame
,
88
, p.
239
.10.1016/0010-2180(92)90034-M
4.
Lam
,
S. H.
, and
Goussis
,
D. A.
,
1994
, “
The CSP Method for Simplifying Kinetics
,”
Int. J. Chem. Kinet.
,
26
, pp.
461
486
.10.1002/kin.550260408
5.
Girimaji
,
S. S.
,
1999
, “
Reduction of Large Dynamical Systems by Minimization of Evolution Rate
,”
Phys. Rev. Lett.
,
82
, pp.
2282
2285
.10.1103/PhysRevLett.82.2282
6.
Fraser
,
S. J.
,
1988
, “
The Steady State and Equilibrium Approximations: A Geometrical Picture
,”
J. Chem. Phys.
,
88
, p.
4732
.10.1063/1.454686
7.
Davis
,
M. J.
, and
Skodje
,
R. T.
,
1999
, “
Geometrical Investigation of Low-Dimensional Manifolds in Systems Approaching Equilibrium
,”
J. Chem. Phys.
,
111
, pp.
859
874
.10.1063/1.479372
8.
Turanyi
,
T.
,
1990
, “
Reduction of Large Reaction Mechanisms
,”
New J. Chem.
,
14
(
11
), pp.
795
803
.
9.
Christo
,
F. C.
,
Masri
,
A. R.
, and
Nebot
,
E. M.
,
1996
, “
Artificial Neural Network Implementation of Chemistry With PDF Simulation of
H2CO2
Flames
,”
Combust. Flame
,
106
(
4
), pp.
404
427
.10.1016/0010-2180(95)00250-2
10.
Kaper
,
H. G.
, and
Kaper
,
T. J.
,
2002
, “
Asymptotic Analysis of Two Reduction Methods for Systems of Chemical Reactions
,”
Physica D
,
165
, pp.
66
93
.10.1016/S0167-2789(02)00386-X
11.
Girimaji
,
S. S.
, and
Brau
,
C.
,
2004
, “
Composition-Space Behavior of Diffusion-Reaction Systems
,”
Theor. Comput. Fluid Dyn.
,
17
(
3
), pp.
171
188
.10.1007/s00162-003-0099-8
12.
Gorban
,
A.
, and
Karlin
,
I.
,
2005
,
Invariant Manifolds for Physical and Chemical Kinetics
, (Lecture Notes in Physics),
Springer
,
New York
.
13.
Josyula
,
E.
, and
Bailey
,
W. F.
,
2005
, “
Multiquantum Vibrational Energy Exchanges in Nonequilibrium Hypersonic Flows
,”
Proceedings of the 38th AIAA Thermophysics Conference
, pp.
6
9
.
14.
Girimaji
,
S. S.
,
2001
, “
Lower-Dimensional Manifold (Algebraic) Representation of Reynolds Stress Closure Equations
,”
Theor. Comput. Fluid Dyn.
,
14
(
4
), pp.
259
281
.10.1007/s001620050140
15.
Roussel
,
M. R.
, and
Tang
,
T.
,
2006
, “
The Functional Equation Truncation Method for Approximating Slow Invariant Manifolds: A Rapid Method for Computing Intrinsic Low-Dimensional Manifolds
,”
J. Chem. Phys.
,
125
, p.
214103
.10.1063/1.2402172
16.
Kazantzis
,
N.
, and
Kravaris
,
C.
, 2011, personal communication.
17.
Aref
,
A.
,
1990
, “
Chaotic Advection of Fluid Particles
,”
Philos. Trans. R. Soc. London
,
333
, pp.
273
288
.10.1098/rsta.1990.0161
18.
Roussel
,
M. R.
, and
Fraser
,
S. J.
,
1990
, “
Geometry of the Steady-State Approximation: Perturbation and Accelerated Convergence Methods
,”
J. Chem. Phys.
,
93
, pp.
1072
1081
.10.1063/1.459171
19.
Suman
,
S.
,
Ibrahim
,
A.
, and
Girimaji
,
S.
,
2011
, “
On the Use of Reduced Chemical Kinetics for Hypersonic Transition and Breakdown to Turbulence Computations
,”
Proceedings of the 41st AIAA Fluid Dynamics Conference and Exhibit
.
20.
Roussel
,
M. R.
,
1994
, “
A Rigorous Approach to Steady-State Kinetics Applied to Simple Enzyme Mechanisms
,” Ph.D. thesis,
University of Toronto
,
Toronto
, Canada.
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