Ostrogradsky-Gauss theorem for problems of gas and fluid mechanics

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Ostrogradsky-Gauss theorem for problems of gas and fluid mechanics. / Prozorova, Evelina.

In: Journal of Physics: Conference Series, Vol. 1334, No. 1, 012009, 18.10.2019.

Research output: Contribution to journal › Conference article › peer-review

BibTeX

@article{0c72d206e1c74bcc8971bfada13f71e8,

title = "Ostrogradsky-Gauss theorem for problems of gas and fluid mechanics",

abstract = "Usually the derivation of conservation laws is analyzed using the Ostrogradsky-Gauss theorem for a fixed volume without moving. The theorem is a consequence of the application of the integration in parts at the spatial case. In reality, in mechanics and physics gas and liquid move and not only progressively, but also rotate. Discarding the term means ignoring the velocity circulation over the surface of the selected volume. When taking into account the motion of a gas, the extra-integral term is difficult to introduce into the differential equation. Therefore, to account for all components of the motion, it is proposed to use an integral formulation. Next question is the role of the discreteness of the description of the medium in the kinetic theory and the interaction of the discreteness and {"}continuity{"} of the media is investigated. The question of the relationship between the discreteness of a medium and its description with the help of continuum mechanics arises due to the fact that the distances between molecules in a rarefied gas are finite, the times between collisions are finite, but on definition under calculating derivatives on time and space we deal with infinitely small.",

keywords = "Boltzmann Equations, Chapman-Enskog Method, Discrete media, Ostrogradsky-Gauss theorem",

author = "Evelina Prozorova",

year = "2019",

month = oct,

day = "18",

doi = "10.1088/1742-6596/1334/1/012009",

language = "English",

volume = "1334",

journal = "Journal of Physics: Conference Series",

issn = "1742-6588",

publisher = "IOP Publishing Ltd.",

number = "1",

note = "3rd International Conference on Mathematical Methods and Computational Techniques in Science and Engineering, MMCTSE 2019 ; Conference date: 23-02-2019 Through 25-02-2019",

}

RIS

TY - JOUR

T1 - Ostrogradsky-Gauss theorem for problems of gas and fluid mechanics

AU - Prozorova, Evelina

PY - 2019/10/18

Y1 - 2019/10/18

N2 - Usually the derivation of conservation laws is analyzed using the Ostrogradsky-Gauss theorem for a fixed volume without moving. The theorem is a consequence of the application of the integration in parts at the spatial case. In reality, in mechanics and physics gas and liquid move and not only progressively, but also rotate. Discarding the term means ignoring the velocity circulation over the surface of the selected volume. When taking into account the motion of a gas, the extra-integral term is difficult to introduce into the differential equation. Therefore, to account for all components of the motion, it is proposed to use an integral formulation. Next question is the role of the discreteness of the description of the medium in the kinetic theory and the interaction of the discreteness and "continuity" of the media is investigated. The question of the relationship between the discreteness of a medium and its description with the help of continuum mechanics arises due to the fact that the distances between molecules in a rarefied gas are finite, the times between collisions are finite, but on definition under calculating derivatives on time and space we deal with infinitely small.

AB - Usually the derivation of conservation laws is analyzed using the Ostrogradsky-Gauss theorem for a fixed volume without moving. The theorem is a consequence of the application of the integration in parts at the spatial case. In reality, in mechanics and physics gas and liquid move and not only progressively, but also rotate. Discarding the term means ignoring the velocity circulation over the surface of the selected volume. When taking into account the motion of a gas, the extra-integral term is difficult to introduce into the differential equation. Therefore, to account for all components of the motion, it is proposed to use an integral formulation. Next question is the role of the discreteness of the description of the medium in the kinetic theory and the interaction of the discreteness and "continuity" of the media is investigated. The question of the relationship between the discreteness of a medium and its description with the help of continuum mechanics arises due to the fact that the distances between molecules in a rarefied gas are finite, the times between collisions are finite, but on definition under calculating derivatives on time and space we deal with infinitely small.

KW - Boltzmann Equations

KW - Chapman-Enskog Method

KW - Discrete media

KW - Ostrogradsky-Gauss theorem

UR - http://www.scopus.com/inward/record.url?scp=85077592233&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1334/1/012009

DO - 10.1088/1742-6596/1334/1/012009

M3 - Conference article

AN - SCOPUS:85077592233

VL - 1334

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012009

T2 - 3rd International Conference on Mathematical Methods and Computational Techniques in Science and Engineering, MMCTSE 2019

Y2 - 23 February 2019 through 25 February 2019

ER -

ID: 51709641