# Solution of Navier-Stokes equations

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 Revision as of 20:29, 15 December 2005 (view source)Tsaad (Talk | contribs) (fixed dot product notation)← Older edit Revision as of 22:30, 20 December 2005 (view source)Ihabsraj (Talk | contribs) Newer edit → Line 25: Line 25: == Coupled Solver == == Coupled Solver == + # Solve the system of momentum and pressure equations in one go (u,v,w,p) + # Solve transport equations for other scalars ---- ---- Return to [[Numerical methods | Numerical Methods]] Return to [[Numerical methods | Numerical Methods]]

## Revision as of 22:30, 20 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

## 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

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