The G-Scheme: A framework for multi-scale adaptive model reduction

Valorani, Mauro; Paolucci, Samuel

doi:10.1016/j.jcp.2009.03.011

Cited by 58 publications

(24 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…propane, still at sample #170. As noted above, only few modes contribute to the range of active scales and, consequently, the most significant reactions to the active dynamics are those contributing to these few modes (all reactions with a large CSP Participation index to the important modes for xs), as already discussed in [23]. Note from Figs.…”

Section: Propane and N-heptane Ignitionmentioning

confidence: 56%

See 1 more Smart Citation

Dynamical system analysis of ignition phenomena using the Tangential Stretching Rate concept

Valorani

Paolucci

Martelli

et al. 2015

Combustion and Flame

View full text Add to dashboard Cite

We analyze ignition phenomena by resorting to the stretching rate concept formerly introduced in the study of dynamical systems. We construct a Tangential Stretching Rate (TSR) parameter by combining the concepts of stretching rate with the decomposition of the local tangent space in eigen-modes. The main feature of the TSR is its ability to identify unambiguously the most energetic scale at a given space location and time instant. The TSR depends only on the local composition of the mixture, its temperature and pressure. As such, it can be readily computed during the post processing of computed reactive flow fields, both for spatially homogeneous and in-homogenous systems.\ud \ud Because of the additive nature of the TSR, we defined a normalized participation index measuring the relative contribution of each mode to the TSR. This participation index to the TSR can be combined with the mode amplitude participation Index of a reaction to a mode – as defined in the Computational Singular Perturbation (CSP) method – to obtain a direct link between a reaction and TSR. The reactions having both a large participation index to the TSR and a large CSP mode amplitude participation index are those contributing the most to both the explosive and relaxation regimes of a reactive system. This information can be used for both diagnostics and for the simplification of kinetic mechanisms.\ud \ud We verified the properties of the TSR with reference to three nonlinear planar models (one for isothermal branched-chain reactions, one for a non-isothermal, one-step system, and for non-isothermal branched-chain reactions), to one planar linear model (to discuss issues associated with non-normality), and to test problems involving hydro-carbon oxidation kinetics.\ud \ud We demonstrated that the reciprocal of the TSR parameter is the proper characteristic chemical time scale in problems involving multi-step chemical kinetic mechanisms, because (i) it is the most relevant time scale during both the explosive and relaxation regimes and (ii) it is intrinsic to the kinetics, that is, it can be identified without the need of any ad hoc assumption

show abstract

Section: Propane and N-heptane Ignitionmentioning

confidence: 56%

“…; N), such that T x ¼ F TSR a A TSR a S TSR . This threefold decomposition is analogous to that employed in the G-Scheme framework proposed in [23]. In the CSP method, the contribution of the M fastest modes (r ¼ 1; .…”

Section: Stretching Rates and Eigenvaluesmentioning

confidence: 98%

Dynamical system analysis of ignition phenomena using the Tangential Stretching Rate concept

Valorani

Paolucci

Martelli

et al. 2015

Combustion and Flame

View full text Add to dashboard Cite

show abstract

“…1.3 Grid approximation of the relaxation redistribution method 4. The G-scheme, which is discussed in [61], the main idea is based on resolving only a range of active time scales and neglect very-slow and very-fast timescales. Therefore, a general idea of the numerical solution is obtained using practical error tolerances, by which a numerical solution is approximating an exact solution.…”

Section: Alternative Modern Systematic Model Reduction Methods Of Mulmentioning

confidence: 99%

General Principles

Geiser¹

2015

Multicomponent and Multiscale Systems

View full text Add to dashboard Cite

In the general principle, we give an overview of the recently used methods and schemes to solve multicomponent and multiscale systems. While multicomponent systems are evolution equations based on each single species, which are coupled with the other species, e.g. with reaction-, diffusion-processes, multiscale systems are evolution equations based on different scales for each species, e.g. macroscopicor microscopic scale. We give the general criteria for practically performing the different splitting and multiscale methods, such that a modification to practical applications of the splitting schemes to a real-life problem can be done. Multicomponent SystemsIn the following, we deal with multicomponent systems. Multicomponent systems concentrate on disparate components in the underlying multiscale models, while they can be coupled by linear or nonlinear functions or differential systems, e.g. reactions or transport phenomena. Often, also different scales are important to resolve to understand the interactions of the different components. Here, we have to apply multicomponent schemes that are also related to disparate spatial and timescales to resolve such complexities, see algorithmic ideas of multicomponent problems in [1].In the following sections, we concentrate on modelling or algorithmical aspects of multicomponent systems for the following applications:• Multicomponent flows, see [2,3].• Multicomponent transport, see [1,4].We simulate the flow and transport systems based on their interactions with the different components. Hence, we allow to study weakly or strongly coupled components in the underlying modelling equation systems. Multicomponent FlowsThe class of multicomponent flows can be defined as a mixture of different chemical species on a molecular level, which are flown with the same velocity and temperature, The modelling of such behaviours is important in engineering, e.g. reactor design (Chemical vapour deposition reactors, see [6]) in chemical engineering. Such processes are very complex, while different physical processes occur, e.g. injection, heating, mixturing, homogeneous and heterogeneous chemistry and further, see [7].In the following, we present some typical problems in multicomponent flow problems:• Ionized Species, e.g. plasma problems, see [4].• Combustion of oil, coal or natural gas, see [8].• Chemical reaction processes in chemical engineering, see [6,9,10].• Atmospheric pollution, see [11].Remark 1.1 In the different applications, the term multiphase flow is often used. Here, we define multiphase flows where the phases are immiscible and not chemically related, see [2,12]. So each phase has a separately defined volume fraction and velocity field. Therefore, also the conservation equations for the flow of each species and their interchange between the phases are different from the multicomponent flow. Here, one is taken into account to define a common pressure field, while each phase is related to the gradient of this field and its volume fraction, see [13]. The applications a...

show abstract

“…However, the necessity to include the full geometry of the combustor obliges to adopt reduced or simplified kinetic schemes to make affordable the computational effort. Usually, reduced kinetic schemes are selected on the basis of the ability to reproduce global parameters like the global burning rate or the laminar flame velocity, rarely with a proper assessment of the ability to reproduce dynamical properties too [32,33]. The ability to reproduce dynamical behavior is taken into consideration in the several numerical studies of flame ignition and quenching.…”

Section: General Aspectsmentioning

confidence: 99%

Non-Linear Response to Periodic Forcing of Methane-Air Global and Detailed Kinetics in Continuous Stirred Tank Reactors Close to Extinction Conditions

Marra

Acampora²,

Martelli³

2015

International Journal of Spray and Combustion Dynamics

View full text Add to dashboard Cite

This paper focus on the behavior of a continuous stirred tank reactor (CSTR) subject to perturbations of finite amplitude and frequency. Two main objectives are pursued: to determine the extinction line in the equivalence ratio (ϕ) -residence time (τ) plane, fixed the thermodynamic state conditions; and to characterize the response of the chemical system to periodic forcing of the residence time. Transient simulations of combustion of methane with air, using both global single-step and detailed chemical kinetic mechanisms, have been conducted and the corresponding asymptotic solutions analyzed. Results indicate very different dynamical behaviors, posing the issue of a proper choice of the kinetic scheme for the numerical study of combustion oscillations.

show abstract

The G-Scheme: A framework for multi-scale adaptive model reduction

Cited by 58 publications

References 27 publications

Dynamical system analysis of ignition phenomena using the Tangential Stretching Rate concept

Dynamical system analysis of ignition phenomena using the Tangential Stretching Rate concept

General Principles

Non-Linear Response to Periodic Forcing of Methane-Air Global and Detailed Kinetics in Continuous Stirred Tank Reactors Close to Extinction Conditions

Contact Info

Product

Resources

About