Tag Info

Questions about solution methods of the Navier-Stokes equations, related physical constants and non-dimensional number. Also special methods to solve the equations including the assumptions and their implementation in order to simplify them. Also, questions regarding modelling of the non-linear term, coefficients of these model can be subjective of this title.

Wiki Quote: In physics, the Navier–Stokes equations [navˈjeː stəʊks], named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing viscous flow.

The Equation

Non-dimensional Navier-Stokes Equation, also known as conservation of momentum (in quite general form)

$\frac{\partial\mathbf{u}}{\partial t}+\mathbf{\left(u\centerdot\nabla\right)u}=-\mathbf{\nabla}p+\frac{1}{Re}\nabla^{2}\mathbf{u}+f$

where

$\mathbf{u}$ is velocity vector

$\mathbf{p}$ is pressure

$f$ external forces (gravity, magnetic field, etc.)