# Solution of Navier-Stokes equations

(Difference between revisions)
 Revision as of 23:07, 20 December 2005 (view source)Jola (Talk | contribs)m (removed some signatures)← Older edit Revision as of 23:08, 20 December 2005 (view source)Jola (Talk | contribs) (removed extra spaces (we should not use extra line-feeds like this...))Newer edit → Line 7: Line 7: # Non linearity of momentum equations # Non linearity of momentum equations # Pressure-velocity coupling # Pressure-velocity coupling - - - ==Segregated Solver== ==Segregated Solver== - === The solution scheme === === The solution scheme === Line 20: Line 16: ## Correct fluxes and velocities ## Correct fluxes and velocities # Solve transport equations for other scalars # Solve transport equations for other scalars - - == Coupled Solver == == Coupled Solver ==

## Revision as of 23:08, 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 Momentum equations- Pressure equation system in one go (u,v,w,p)
2. Solve transport equations for other scalars