Solution of Navier-Stokes equations

For the incompressible flows, the Navier-Stokes equation could be written in the form:

$\nabla \cdot \vec U = 0$
${{\partial \vec U} \over {\partial t}} + \nabla \cdot \left( {\vec U\vec U} \right) - \nabla \cdot\left( {\nu \nabla \vec U} \right) = - \nabla p$

There are two important issues regarding Navier-Stokes equations:

1. Non linearity of momentum equations
2. Pressure-velocity coupling

Segregated Solver

The solution scheme

1. Solve Momentum equations (u,v,w)
2. Solve pressure correction equation
1. Correct fluxes and velocities
3. Solve transport equations for other scalars

Coupled Solver

1. Solve the system of momentum and pressure equations in one go (u,v,w,p)
2. Solve transport equations for other scalars