Novel Analytical Molecular Dynamics Technique for Solving Fluid Dynamics Problems

A novel analytical molecular dynamics technique (NAMDT), based on 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 solving fluid dynamics problems. The integro-differential balance
equations for mass, momentum, and energy are derived by applying four significant steps: assigning to model
gas properties that differ from the properties typically assigned to the ideal gas, imitating the movement of each
particle/molecule of the model gas by specifying to each particle a ballistic trajectory, gathering that movements
into analytically defined macro quantities characterizing the model gas flow, and applying the BPPBS. The
integro-differential balance equations for mass and momentum were further approximated for the collisiondominated
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. We were surprised to observe
that our converted differential forms look identically to the Navier-Stokes equations. This finding has led us to
conclude 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 mathematical
verifications demonstrating the feasibility of the proposed method and an example of its computer
implementation are presented here. The NAMDT will be highly useful not only 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. The method also delivers a new
basis for predicting the dynamic evolution of the model gas system by considering a pre-established or known
dynamic history of the system during a pre-initial period.