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.
Highlights
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
We introduce newly discovered Ballistic Principle of the Property Balance in the Space occupied by the gas, applying of which is expected to simplify and reduce computations in applications dealing with modeling of fluid dynamics problems
1) Modeling of fluid dynamics problems by the novel analytical molecular dynamics technique (NAMDT) is based on the recognition that each particle composing the model gas travels with a probability between any of two points in space occupied by the model gas while following a ballistic trajectory governed by a law of motion in free space
Summary
Mathematicians and physicists consider the recent advancement of the method of the lattice Boltzmann (LB) equation as a significant alternative to standard computational fluid dynamics [6] This approach consists in modeling “the physical reality at a mesoscopic level: the generic features of microscopic processes can be expressed through simple rules, from which the desired macroscopic behavior emerges as a collective effect of the interactions between the many elementary components [7].”. In the validation test 4.6, we supported the proposed approach by revealing that, in the collision-dominated flow regime, the differential equations, which were converted from the integro-differential mass and momentum balance equations, are identical to the corresponding Navier-Stokes equations.
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