An Optimization Approach to Kinetic Model Reduction for Combustion Chemistry

Lebiedz, Dirk; Siehr, Jochen

doi:10.1007/s10494-014-9532-x

Cited by 3 publications

(2 citation statements)

References 42 publications

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“…The work of Ginoux et al is of particular significance in the context of this paper, it supported our inspiration to work on topics presented here although we have been concerned with differential geometry ideas in the context of slow invariant manifolds since some years [32] without knowing about Ginoux's work. Our model reduction technique is based on a variational principle by using a trajectory-based optimization approach is proposed by Lebiedz et al [27,31,32,33,35,34], which is supposed to be applied to kinetic models in combustion chemistry [28,29]. The recently published work of Lebiedz and Unger [30] discusses and exploits common ideas and brings together concepts of several model reduction approaches.…”

Section: Introductionmentioning

confidence: 99%

Towards Differential Geometric Characterization of Slow Invariant Manifolds in Extended Phase Space: Sectional Curvature and Flow Invariance

Heiter¹,

Lebiedz²

2018

SIAM J. Appl. Dyn. Syst.

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Some model reduction techniques for multiple time-scale dynamical systems make use of the identification of low dimensional slow invariant attracting manifolds (SIAM) in order to reduce the dimensionality of the phase space by restriction to the slow flow. The focus of this work is on a proposition and discussion of a general viewpoint using differential geometric concepts for submanifolds to deal with slow invariant manifolds in an extended phase space. The motivation is a coordinate independent formulation of the manifold properties and its characterization problem treating the manifold as intrinsic geometric object. We formulate a computationally verifiable necessary condition for the slow invariant manifold graph stated in terms of a differential geometric view on the invariance property. Its application to example systems is illustrated. In addition, we present some ideas and investigations concerning the search for sufficient, differential geometric conditions characterizing slow invariant manifolds based on our previously developed variational principle.

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Section: Introductionmentioning

confidence: 99%

Towards Differential Geometric Characterization of Slow Invariant Manifolds in Extended Phase Space: Sectional Curvature and Flow Invariance

Heiter¹,

Lebiedz²

2018

SIAM J. Appl. Dyn. Syst.

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“…Other constructive methods are based on the iterative solution of the partial differential equations defining the slow manifold (e.g. 13 ), on finding the invariant manifold connecting the equilibrium state to (usually unphysical) saddle points 5,14 , and on trajectoryoptimization variational approaches 12,15 , which was recently applied for the construction of a two-dimensional SIM for syngas combustion 16 .…”

Section: Introductionmentioning

confidence: 99%

The global relaxation redistribution method for reduction of combustion kinetics

Kooshkbaghi

Frouzakis

Chiavazzo

et al. 2014

The Journal of Chemical Physics

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An algorithm based on the Relaxation Redistribution Method (RRM) is proposed for constructing the Slow Invariant Manifold (SIM) of a chosen dimension to cover a large fraction of the admissible composition space that includes the equilibrium and initial states. The manifold boundaries are determined with the help of the Rate Controlled Constrained Equilibrium method, which also provides the initial guess for the SIM. The latter is iteratively refined until convergence and the converged manifold is tabulated. A criterion based on the departure from invariance is proposed to find the region over which the reduced description is valid. The global realization of the RRM algorithm is applied to constant pressure auto-ignition and adiabatic premixed laminar flames of hydrogen-air mixtures.

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On unifying concepts for trajectory-based slow invariant attracting manifold computation in kinetic multiscale models

Lebiedz¹,

Unger²

2016

Mathematical and Computer Modelling of Dynamical Systems

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Chemical kinetic models in terms of ordinary differential equations correspond to finite dimensional dissipative dynamical systems involving a multiple time scale structure. Most dimension reduction approaches aimed at a slow mode-description of the full system compute approximations of low-dimensional attracting slow invariant manifolds and parameterize these manifolds in terms of a subset of chosen chemical species, the reaction progress variables. The invariance property suggests a slow invariant manifold to be constructed as (a bundle of) solution trajectories of suitable ordinary differential equation initial or boundary value problems. The focus of this work is on a discussion of fundamental and unifying geometric and analytical issues of various approaches to trajectory-based numerical approximation techniques of slow invariant manifolds that are in practical use for model reduction in chemical kinetics. Two basic concepts are pointed out reducing various model reduction approaches to a common denominator. In particular, we discuss our recent trajectory optimization approach in the light of these two concepts. We relate both of them in a variational boundary value viewpoint, propose a Hamiltonian formulation and conjecture its relation to conservation laws, (partial) integrability and symmetry issues as underlying fundamental principles and potentially unifying elements of diverse dimension reduction approaches.

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An Optimization Approach to Kinetic Model Reduction for Combustion Chemistry

Cited by 3 publications

References 42 publications

Towards Differential Geometric Characterization of Slow Invariant Manifolds in Extended Phase Space: Sectional Curvature and Flow Invariance

Towards Differential Geometric Characterization of Slow Invariant Manifolds in Extended Phase Space: Sectional Curvature and Flow Invariance

The global relaxation redistribution method for reduction of combustion kinetics

On unifying concepts for trajectory-based slow invariant attracting manifold computation in kinetic multiscale models

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