Method of invariant grid for model reduction of hydrogen combustion

Chiavazzo, Eliodoro; Karlin, Iliya V.; Frouzakis, Christos E.; Boulouchos, Konstantinos

doi:10.1016/j.proci.2008.05.014

Cited by 13 publications

(11 citation statements)

References 13 publications

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“…The phase-space probability density f [N ] satisfies the Liouville equation [50], although its use is not very practical due to the curse of dimensionality (6N , where N can be of the other of Avogadro number). For computing thermodynamic quantities, it proves useful to consider some asymptotic equilibrium limit (determined by attracting low-dimensional manifolds for trajectories in the phase-space [51,52,53,54,55,56]), namely f (e) [N ] , which becomes a function of the timevarying coordinates and macroscopic momenta/quantities. From the practical point of view, in most of the fluid dynamic problems (excluding rarefaction effects), the characteristic time to reach the equilibrium limit is extremely short (in comparison with fluid dynamic ones).…”

Section: Methodsmentioning

confidence: 99%

The notion of energy through multiple scales: From a molecular level to fluid flows and beyond

Asinari

Chiavazzo

2014

Energy

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In the present paper, we review the consistent definition of macroscopic total energy in classical fluid mechanics, as a function of the microscopic canonical Hamiltonian field, based on a Lennard-Jones model with some spatially varying external field. The macroscopic total energy (sum of mechanical and internal energy) is proved to be equal to the equilibrium ensemble-averaged Hamiltonian. In particular, the conditions for including the effects of the external field both in the macroscopic potential energy and in the internal energy are discussed. We present the notion of energy as defined in different scientific communities, starting from the standard macroscopic systems all the way down to small ones, which are gaining an increasing popularity.

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Section: Methodsmentioning

confidence: 99%

The notion of energy through multiple scales: From a molecular level to fluid flows and beyond

Asinari

Chiavazzo

2014

Energy

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“…A related approach termed the method of invariant grids (MIG) is also discussed in Gorban and Karlin (2003), Gorban et al (2004a, c), Chiavazzo et al (2007Chiavazzo et al ( , 2009 based on the method of invariant manifold (MIM). In MIG, a quasi-equilibrium approach is used to define a first approximation to the SIM on a grid in concentration space, and then improved estimations of the SIM are obtained using either Newton iteration or relaxation methods.…”

Section: Calculation Of Slow Invariant Manifoldsmentioning

confidence: 99%

Analysis of Kinetic Reaction Mechanisms

Turányi¹,

Tomlin²

2014

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“…5. The method of Invariant Grid (MIG), which is discussed in [62,63], is based on the model reduction concept of slow manifolds (SIM). The MIG algorithm is based on the idea to approximate the SIM by a set of grid nodes in the invariant grid (concentration space).…”

Section: Alternative Modern Systematic Model Reduction Methods Of Mulmentioning

confidence: 99%

General Principles

Geiser¹

2015

Multicomponent and Multiscale Systems

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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...

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Method of invariant grid for model reduction of hydrogen combustion

Cited by 13 publications

References 13 publications

The notion of energy through multiple scales: From a molecular level to fluid flows and beyond

The notion of energy through multiple scales: From a molecular level to fluid flows and beyond

Analysis of Kinetic Reaction Mechanisms

General Principles

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