Mathematical concepts and their physical foundation in the nonstandard analysis theory of turbulence |
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Authors: | Wu Feng |
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Institution: | Department of Mechanics and Mechanical Engineering, University of Science and\\ Technology of China, Hefei 230026, China |
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Abstract: | Main mathematical concepts and their physical foundation in the
nonstandard analysis theory of turbulence are presented and
discussed. The underlying fact is that there does not exist the
absolute zero fluid-volume. Therefore, the physical object
corresponding to the absolute point is just the uniform
fluid-particle. The fluid-particle, in general, corresponds to the
monad. The uniform fluid-particle corresponds to the uniform monad,
while the nonuniform fluid-particle to the nonuniform monad. There
are two kinds of the differentiations, one is based on the absolute
point, and the other based on the monad. The former is adopted in
the Navier--Stokes equations, and the latter in the fundamental
equations presented in this paper for the nonstandard analysis
theory of turbulence. The continuity of fluid is elucidated by
virtue of the concepts of the fluid-particle and fluid-particle at a
lower level. Furthermore, the characters of the continuity in two
cases, i.e. in the standard and nonstandard analyses, are presented
in this paper. And the difference in discretization between the
Navier--Stokes equations and the fundamental equations given herein
is also pointed out. |
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Keywords: | turbulence monad fluid-particle at a lower level nonstandard analysis theory of
turbulence |
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