An inverse kinetic theory for the incompressible Navier–Stokes equations

An inverse kinetic theory applying specifically to incompressible Newtonian fluids which permits us to avoid the N2 algorithmic complexity of the Poisson equation for the fluid pressure is presented. The theory is based on the construction of a suitable kinetic equation in phase space, which permits us to determine exactly the fluid equations by means of the velocity moments of the kinetic distribution function. It is found that the fluid pressure can also be determined as a moment of the distribution function without solving the Poisson equation, as is usually required in direct solution methods for the incompressible fluid equations. Finally, the dynamical system, underlying the incompressible Navier–Stokes equations and advancing in time the fluid fields, has been also identified and proven to produce an unique set of fluid equations.