# Solution of Navier-Stokes equations

(Difference between revisions)
 Revision as of 07:23, 3 October 2005 (view source)Zxaar (Talk | contribs)← Older edit Revision as of 20:29, 15 December 2005 (view source)Tsaad (Talk | contribs) (fixed dot product notation)Newer edit → Line 1: Line 1: For the incompressible flows, the Navier-Stokes equation could be written in the form:
For the incompressible flows, the Navier-Stokes equation could be written in the form:
:$:[itex] - \nabla \bullet \vec U = 0$
+ \nabla  \cdot \vec U = 0 [/itex]
- :${{\partial \vec U} \over {\partial t}} + \nabla \bullet \left( {\vec U\vec U} \right) - \nabla \bullet \left( {\nu \nabla \vec U} \right) = - \nabla p$ + :${{\partial \vec U} \over {\partial t}} + \nabla \cdot \left( {\vec U\vec U} \right) - \nabla \cdot\left( {\nu \nabla \vec U} \right) = - \nabla p$ There are two important issues regarding Navier-Stokes equations:
There are two important issues regarding Navier-Stokes equations:

## Revision as of 20:29, 15 December 2005

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