Novel Analytical Molecular Dynamics Technique for Solving Fluid Dynamics Problems
To simplify and minimise computations in applications dealing with fluid dynamics issues, a novel analytical molecular dynamics technique (NAMDT), based on a newly discovered Ballistic Theory of the Property Balance in Space (BPPBS) occupied by gas, is implemented. By applying four significant steps, the integro-differential balance equations for mass, momentum, and energy are derived: assigning to model gas properties that vary from the properties usually assigned to the ideal gas, imitating the movement of each model gas particle/molecule by defining a ballistic trajectory for each particle, collecting those movements into analytically specified mac For the collision-dominated flow regime, the integro-differential equilibrium equations for mass and momentum have been further approximated. Then, by the vector differentiation process, they were reduced to the corresponding vector differential equations with subsequent removal of the terms belonging to the original equation. It has been shown that the derived vector differential equations of mass and momentum balance are similar to the corresponding Navier-Stokes equations in the collision-dominated flow regime. We were shocked to observe that the Navier-Stokes equations look similar to our transformed differential forms. This result led us to conclude that the formulated integro-differential forms of equilibrium are precise implicit solutions to the corresponding Navier-Stokes equations in the collision-dominated flow regime. Here are six additional mathematical verifications showing the viability of the approach proposed and an example of its device implementation.
Dr. Nikolai Kislov
Nano CVD Company, Tampa, Florida, USA.
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