Discrete Velocity Models and Dynamical Systems

Bobylev, A. V.; Bernhoff, Niclas

doi:10.1142/9789812796905_0008

Cited by 20 publications

(32 citation statements)

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“…Extensions to larger normal models (of any finite size) can be obtained by the so-called one-extension method [10,11,13,28]. A one-extension is obtained by, having three velocities from a possible collision, but not the fourth, in the velocity set, add the fourth velocity from the collision to the velocity set and obtain a new linearly independent (with respect to previously existing collisions) collision.…”

Section: Construction Of a Family Of Supernormal Dvms For Mixturesmentioning

confidence: 99%

“…Another important issue is the one of approximating the full Boltzmann equation for mixtures by DVMs. One possible way to address this problem is provided in [10]. In [10] the same velocity set is used for different species.…”

Section: Examplementioning

confidence: 99%

“…One possible way to address this problem is provided in [10]. In [10] the same velocity set is used for different species. This is not the case in the DVMs constructed above.…”

Section: Examplementioning

confidence: 99%

“…We present the half-space problems and applicable existence results to our case, without any proofs, since they can be found elsewhere [5,6,9]. The results obtained in [6] can also be generalized by similar methods.…”

Section: Introductionmentioning

confidence: 98%

“…It was for a while conjectured that all normal DVMs could be obtained from some minimal models by so called one-extensions [10,11,13,28]. A one-extension is obtained by, having already three velocities (out of four) from a possible collision in a normal DVM, adding the fourth velocity and so obtaining a new normal DVM, with one more velocity.…”

Section: Introductionmentioning

confidence: 99%

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Discrete Velocity Models for Mixtures Without Nonphysical Collision Invariants

Bernhoff

Vinerean

2016

J Stat Phys

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An important aspect of constructing discrete velocity models (DVMs) for the Boltzmann equation is to obtain the right number of collision invariants. It is a well-known fact that DVMs can also have extra collision invariants, so called spurious collision invariants, in plus to the physical ones. A DVM with only physical collision invariants, and so without spurious ones, is called normal. For binary mixtures also the concept of supernormal DVMs was introduced, meaning that in addition to the DVM being normal, the restriction of the DVM to any single species also is normal. Here we introduce generalizations of this concept to DVMs for multicomponent mixtures. We also present some general algorithms for constructing such models and give some concrete examples of such constructions. One of our main results is that for any given number of species, and any given rational mass ratios we can construct a supernormal DVM. The DVMs are constructed in such a way that for half-space problems, as the Milne and Kramers problems, but also nonlinear ones, we obtain similar structures as for the classical discrete Boltzmann equation for one species, and therefore we can apply obtained results for the classical Boltzmann equation.

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Section: Construction Of a Family Of Supernormal Dvms For Mixturesmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

“…One possible way to address this problem is provided in [10]. In [10] the same velocity set is used for different species. This is not the case in the DVMs constructed above.…”

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Discrete Velocity Models for Mixtures Without Nonphysical Collision Invariants

Bernhoff

Vinerean

2016

J Stat Phys

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Half-Space Problems for the Boltzmann Equation of Multicomponent Mixtures

Bernhoff

2022

Springer INdAM Series

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Half-Space Problem for the Discrete Boltzmann Equation: Condensing Vapor Flow in the Presence of a Non-condensable Gas

Bernhoff

2012

J Stat Phys

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We consider a non-linear half-space problem related to the condensation problem for the discrete Boltzmann equation and extend some known results for a single-component gas to the case when a non-condensable gas is present. The vapor is assumed to tend to an assigned Maxwellian at infinity, as the non-condensable gas tends to zero at infinity. We assume that the vapor is completely absorbed and that the non-condensable gas is diffusively reflected at the condensed phase and that the vapor molecules leaving the condensed phase are distributed according to a given distribution. The conditions, on the given distribution, needed for the existence of a unique solution of the problem are investigated. We also find exact solvability conditions and solutions for a simplified six+four-velocity model, as the given distribution is a Maxwellian at rest, and study a simplified twelve+six-velocity model.Keywords Boltzmann equation · boundary layers · discrete velocity models · half-space problem · non-condensable gasIn this paper we consider the condensation problem for a single-component gas or vapor when a non-condensable gas is present [15]. Formulation and motivation of the problem can be found in [15]. The vapor is assumed to tend to an assigned Maxwellian M A ∞ , with a flow velocity towards the condensed phase, at infinity, while the non-condensable gas tends to zero at infinity.

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Discrete Velocity Models and Dynamical Systems

Cited by 20 publications

References 0 publications

Discrete Velocity Models for Mixtures Without Nonphysical Collision Invariants

Discrete Velocity Models for Mixtures Without Nonphysical Collision Invariants

Half-Space Problems for the Boltzmann Equation of Multicomponent Mixtures

Half-Space Problem for the Discrete Boltzmann Equation: Condensing Vapor Flow in the Presence of a Non-condensable Gas

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