Abstract
The conservation laws of continuum mechanics and of the kinetic theory with the influence of the angular momentum and associated with its rotation of the elementary volume are considered, the variant of accounting lag is investigated for discrete environment. The analysis of the recording of the Lagrangian function for the collective interaction of the particles with the change of the center of inertia of the moving particles and the effect influence of the angular momentum were used. The equations for gas are calculated from the modified Boltzmann equation and the phenomenological theory. For a rigid body the equations were used of the phenomenological theory, but their interpretation was changed. The nonsymmetric stress tensor was obtained. The Boltzmann equation is written with an additional summand. This situation is typical for discrete environment as the transition from discrete to continuous environment is a key to the issue of mechanics. Summary records of all effects lead to a cumbersome system of equations and therefore require the selection of main effects in a particular situation. The Hilbert paradox was being solved. The simplest problem of the boundary layer continuum (the Falkner-Skan task) and the kinetic theory are discussed. A draw attention at the delay process would be suggested for the description of discrete environment. Results are received for some special cases.
Highlights
The conservation laws of continuum mechanics and of the kinetic theory with the influence of the angular momentum and associated with its rotation of the elementary volume are considered, the variant of accounting lag is investigated for discrete environment
6) Isolation of large eddies with the addition of the flow pattern inside the grid cell by further study the model selected inside the cell Before proceeding to the solution of specific problems, we present a quote from the Loitsyanskii book [12]: “The current lines of pulsating movement of cross streamlines of the mean flow, penetrate from one layer to another, and create the stirring—it is called a molar or turbulent mixing—accompanied by the transport through the boundary between the layers of momentum, energy, heat, and other mechanical or thermodynamic parameters of the mean flow liquid
Influence of the angular momentum is investigated and, as consequence, nonsymmetry of stress tensor is received for elementary volume
Summary
There were previously obtained modified energy equation of motion, continuity and momentum for particles without structure, taking into account effects of the change of the angular momentum in the elementary volume. It should be noted that for the kinetic theory (the Boltzmann equation) the law of conservation of angular momentum does not hold. In this paper we numerically investigate the influence of small perturbations of vertical velocity on the longitudinal velocity in the modified Falkner-Skan problem to reflect changes the influence of the angular momentum in the elementary volume This modified task is difficult for the numerical solution, because the system of equations contain derivatives of the third order, being at the same time singular with small parameter near derivatives, as Navie-Stokes equations. To study the delay in the kinetic theory is necessary due to the finiteness of the interaction time between the molecules and the definition of a derivative
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