BGK-type models in strong reaction and kinetic chemical equilibrium regimes

Monaco, Roberto; Bianchi, M. Pandolfi; Soares, Ana Jacinta

doi:10.1088/0305-4470/38/48/012

Cited by 11 publications

(13 citation statements)

References 20 publications

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“…These problems can be handled in the frame of the continuum theory of fluids [3], but a rigorous derivation of the relevant fluid-dynamic equations from the deeper knowledge allowed by a kinetic approach is highly desirable, also as consistent justification or correction of the most common macroscopic descriptions [4]. Most of the kinetic literature, however, is still restricted to the simplified case of mono-atomic particles, which, in spite of its limitation, reproduces interesting results with good agreement with reality and expectation [5][6][7]. On the other hand it is clear that gases involved in practical applications are typically made up by polyatomic molecules, not su ciently described by the motion of their center of mass, and that the situation becomes even more complicated when chemical interactions with additional exchange of mass among species may take place [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic limits of kinetic equations for polyatomic and reactive gases

Bisi

Spiga

2017

Communications in Applied and Industrial Mathematics

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Starting from a kinetic BGK-model for a rarefied polyatomic gas, based on a molecular structure of discrete internal energy levels, an asymptotic Chapman-Enskog procedure is developed in the asymptotic continuum limit in order to derive consistent fluid-dynamic equations for macroscopic fields at Navier-Stokes level. In this way, the model allows to treat the gas as a mixture of mono-atomic species. Explicit expressions are given not only for dynamical pressure, but also for shear stress, di↵usion velocities, and heat flux. The analysis is shown to deal properly also with a mixture of reactive gases, endowed for simplicity with translational degrees of freedom only, in which frame analogous results can be achieved.

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Section: Introductionmentioning

confidence: 99%

Hydrodynamic limits of kinetic equations for polyatomic and reactive gases

Bisi

Spiga

2017

Communications in Applied and Industrial Mathematics

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“…Furthermore we include a reactive linear term (BGK-like [114][115][116][117]) and obtain a general associated Kramers equation. In Section 3 we expand the solution generalizing a previous result [75] yielding recursive relations (for other expansions in the literature see for example Refs.…”

Section: Introductionmentioning

confidence: 99%

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

Lagos

Simões

2011

Physica A: Statistical Mechanics and its Applications

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a b s t r a c tWe consider a charged Brownian gas under the influence of external and non-uniform electric, magnetic and mechanical fields, immersed in a non-uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To the first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle density, a Smoluchowski-reactive like equation; for the particle's momentum density, a generalized Ohm's-like equation; and for the particle's energy density, a Maxwell-Cattaneo-like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann's entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non-linear reactive kinetics and a mean field approach to interacting Brownian particles.

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“…We remind that, as shown in Section 3, the relaxation algorithm (11) drives velocity distributions towards Maxwellians corresponding to both mechanical and chemical equilibrium. In addition, it does not separate the two processes, and keeps track of the actual microscopic phenomena only through the global inverse relaxation times (30) or (31), in which the two types of encounters are simply summed up, and the same sum can be achieved by different balances of mechanical and chemical contributions. Therefore, the present BGK model is particularly well suited when mechanical and chemical processes share the same level of importance in driving the evolution problem.…”

Section: Numerical Testsmentioning

confidence: 99%

“…The reactive exothermic chemical collision frequency is instead ν 12 34 = 0.5, of the same order of magnitude as elastic collision frequencies. Global collision frequencies are given by formulas (30) with the option A = 0.…”

Section: Numerical Testsmentioning

confidence: 99%

“…Questions related to hydrodynamic limit and transport coefficients have been studied separately by a Chapman-Enskog asymptotic expansion [28]. Of course, this is not the only strategy for a consistent BGK approach to reactive flows; without pretending to be exhaustive, we may quote, in addition to the previous ones, also the recent papers [29,30]. Collision frequencies to be used here include the mechanical…”

Section: Introductionmentioning

confidence: 99%

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