Navier-Stokes

• Navier-Stokes equations are partial differential equations that govern the movement of incompressible fluids
• They constitute the basic equations of fluid dynamics
• Velocity, pressure, temperature, density, and viscosity are the main properties that should be considered simultaneously when conducting a fluid flow examination.
• The equations are based on the laws of conservation
  • Conservation of mass: Continuity equation
  • Conservation of momentum: Newton’s second law
  • Conservation of energy: First law of thermodynamics

$\vec{u}$ - velocity vector $\vec{u}=(u,v,w)$

Conservation of mass, $\nabla \vec{u}=0$

Conservation of momentum (Newton’s second law) $\rho$

Refs §

1. https://www.youtube.com/watch?v=ERBVFcutl3M
2. https://www.simscale.com/docs/simwiki/numerics-background/what-are-the-navier-stokes-equations/