# Solution of Navier-Stokes equations

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For the incompressible flows, the Navier-Stokes equation could be written in the form: <br> | For the incompressible flows, the Navier-Stokes equation could be written in the form: <br> | ||

:<math> | :<math> | ||

- | \nabla \ | + | \nabla \cdot \vec U = 0 </math> <br> |

- | :<math> {{\partial \vec U} \over {\partial t}} + \nabla \ | + | :<math> {{\partial \vec U} \over {\partial t}} + \nabla \cdot \left( {\vec U\vec U} \right) - \nabla \cdot\left( {\nu \nabla \vec U} \right) = - \nabla p </math> |

There are two important issues regarding Navier-Stokes equations: <br> | There are two important issues regarding Navier-Stokes equations: <br> |

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

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

There are two important issues regarding Navier-Stokes equations:

- Non linearity of momentum equations
- Pressure-velocity coupling

## Segregated Solver

### The solution scheme

- Solve Momentum equations (u,v,w)
- Solve pressure correction equation
- Correct fluxes and velocities

- Solve transport equations for other scalars

## Coupled Solver

* Return to Numerical Methods *