TITLE:
Ballistic Principle of the Property Balance in Space and Its Application to Modeling of Fluid Dynamics Problems
AUTHORS:
Nikolai Kislov
KEYWORDS:
Navier-Stokes, Fluid Dynamics, Fluid Flow, Rarefied, Gas
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.6,
June
5,
2020
ABSTRACT: A newly discovered Ballistic Principle of the Property Balance in the Space (BPPBS) occupied by the gas is introduced to simplify and reduce computations in applications dealing with modeling of fluid dynamics problems. The integro-differential balance equations for mass, momentum, and energy, which were formulated by applying the BPPBS, are derived. The integro-differential balance equations for mass and momentum were further approximated for the collision-dominated flow regime. Then they were reduced to the corresponding vector differential equations by the method of vector differentiation with subsequent elimination of the terms belonging to the original equation. It was shown that in the collision-dominated flow regime, the derived vector differential equations of mass and momentum balance are identical to the corresponding Navier-Stokes equations. This finding validates the BPPBS and suggests that, in the collision-dominated flow regime, the formulated integro-differential forms of the balance are exact implicit solutions for corresponding Navier-Stokes equations. Six additional tests demonstrating the feasibility of the proposed method and validity of the BPPBS are presented here. The BPPBS and the methodology discussed here will be highly useful not only as the basis to solve the fluid dynamics problems, but also to model any dynamic system composed of presumably chaotically moving particles/elements, each carrying a specific amount of property/information.