## Solution of Navier-Stokes Equations

Even though the **Navier-Stokes equations** have only a limited number of known analytical solutions, they are amenable to fine-gridded computer modeling. The main tool available for their analysis is **CFD analysis**. CFD is a branch of fluid mechanics that uses numerical analysis and algorithms to solve and analyze problems that involve turbulent fluid flows. It is widely accepted that the **Navier–Stokes equations** (or simplified **Reynolds-averaged Navier–Stokes equations**) are capable of exhibiting turbulent solutions, and these equations are the basis for essentially all CFD codes. It is possible now to achieve approximate, but realistic, CFD results for a wide variety of complex two- and three-dimensional viscous flows.

The **Navier–Stokes equations** are also of great interest in a purely mathematical sense. Unfortunately, the highly intermittent and irregular character of **turbulent flow** **complicates all analyses**. It has not yet been proven that in three dimensions solutions always exist, or that if they do exist, then they are smooth. In fact, general solution of the Navier-Stokes equations with turbulences is often said to be the** “last unsolved problem in classical mathemetical physics.”**

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