Some Paradoxes of Mathematical Theory of Continues Mechanics

Prozorova, Evelina

doi:10.11648/j.ajam.20180601.13

Cited by 2 publications

(1 citation statement)

References 6 publications

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“…The second method of transition is the contraction of the volume to zero and the construction of averages values. Consequently, the tangential component will also give the normal velocity component [22,23].…”

Section: Fig 2 Elementary Volume For Ostrogradsky-gauss Theoremmentioning

confidence: 99%

The Effect of Angular Momentum and Ostrogradsky-Gauss Theorem in the Equations of Mechanics

Prozorova

2020

Wseas Transactions on Fluid Mechanics

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There are many experimental facts that currently cannot be described theoretically. A possible reason is bad mathematical models and algorithms for calculation, despite the many works in this area of research. The aim of this work is to clarificate the mathematical models of describing for rarefied gas and continuous mechanics and to study the errors that arise when we describe a rarefied gas through distribution function. Writing physical values conservation laws via delta functions, the same classical definition of physical values are obtained as in classical mechanics. Usually the derivation of conservation laws is based 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 along a forward path, but also rotate. Discarding the out of integral term means ignoring the velocity circulation over the surface of the selected volume. When taking into account the motion of a gas, this 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. 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 values. We investigate it

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Section: Fig 2 Elementary Volume For Ostrogradsky-gauss Theoremmentioning

confidence: 99%

The Effect of Angular Momentum and Ostrogradsky-Gauss Theorem in the Equations of Mechanics

Prozorova

2020

Wseas Transactions on Fluid Mechanics

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Features of the rarefied gas description in terms of a distribution function

Prozorova¹

2019

J. Phys.: Conf. Ser.

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The aim of the paper is to determine the relationship of the classical model for describing a rarefied gas using the distribution function and its discrete representation. Here we study the role of discreteness in the description of a medium in the kinetic theory and the interrelation between interaction of the discreteness and the “continuity” of a media. The question of the relationship between the discreteness of a medium and its description with the help of continuum mechanics is important both when processing experimental data and when going from a continuum model to discrete one in mechanics and physics. There are many studies devoted to the influence of the transition from a continuous to discrete medium in computational mathematics, but there is no study of inverse processes. The work related to the formulation of conservation laws as conditions of the equilibrium of forces and moments of forces, as well as the action of additional flows on the sides of an elementary volume, was carried out earlier. After refinement, non -symmetric stress tensor was obtained. The method for calculating this tensor was proposed. The equations for a gas were found from the modified Boltzmann equation and from the phenomenological theory. Inaccuracy leading to the symmetry of the stress tensor arises when calculating the Lagrange function of particles as the sum of pairwise interacting particles and the unchanged position of the inertia system center.

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Some Paradoxes of Mathematical Theory of Continues Mechanics

Cited by 2 publications

References 6 publications

The Effect of Angular Momentum and Ostrogradsky-Gauss Theorem in the Equations of Mechanics

The Effect of Angular Momentum and Ostrogradsky-Gauss Theorem in the Equations of Mechanics

Features of the rarefied gas description in terms of a distribution function

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