Stochastic Magnetic Hydrodynamic Hierarchy in a Strong External Magnetic Field

Based on a stochastic microscopic collisional model of the motion of charged particles in a strong external magnetic field, a hierarchy of equations of magnetic hydrodynamics is constructed. The transition to increasingly rough approximations occurs in accordance with a decrease in the dimensioning...

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Bibliographic Details
Published in:Mathematical models and computer simulations 2020-03, Vol.12 (2), p.257-270
Main Authors: Bogomolov, S. V., Esikova, N. B.
Format: Article
Language:English
Subjects:
Charged particles
Computational fluid dynamics
Differential equations
Distribution functions
Exact solutions
Fluid flow
Fluid mechanics
Gas dynamics
Hydrodynamics
Macroscopic equations
Magnetic fields
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Mathematics and Statistics
Random processes
Simulation and Modeling
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Summary:Based on a stochastic microscopic collisional model of the motion of charged particles in a strong external magnetic field, a hierarchy of equations of magnetic hydrodynamics is constructed. The transition to increasingly rough approximations occurs in accordance with a decrease in the dimensioning parameter, similar to the Knudsen number in gas dynamics. The result is stochastic and nonrandom macroscopic equations that differ from the magnetic analog of the Navier–Stokes system of equations, as well as from the systems of magnetic quasi-hydrodynamics. The main feature of this derivation is more accurate velocity averaging due to the analytical solution of stochastic differential equations with respect to the Wiener measure, in the form of which the intermediate meso model is presented in the phase space. This approach differs significantly from the traditional one, which uses not the random process itself but its distribution function. Emphasis is placed on the clarity of assumptions when moving from one level of detail to another, and not on numerical experiments that contain additional approximation errors.
ISSN:2070-0482
2070-0490
DOI:10.1134/S2070048220020039