An exact pressure evolution equation for the incompressible Navier-Stokes equations

In this paper the issue of the determination of the fluid pressure in incompressible fluids is addressed, with particular reference to the search of algorithms which permit to advance in time the fluid pressure without actually solving numerically the Poisson equation. Based on an inverse kinetic approach recently proposed for the incompressible Navier-Stokes equations we intend to prove that an exact evolution equation can be obtained which advances in time self-consistently the fluid pressure. The new equation is susceptible of numerical implementation in Lagrangian CFD simulation codes.