# Solution of Navier-Stokes equations

(Difference between revisions)
 Revision as of 22:30, 20 December 2005 (view source)Ihabsraj (Talk | contribs)← Older edit Revision as of 23:00, 20 December 2005 (view source)Ihabsraj (Talk | contribs) Newer edit → Line 9: Line 9: - + --[[User:Ihabsraj|Ihabsraj]] 16:00, 20 December 2005 (MST)--[[User:Ihabsraj|Ihabsraj]] 16:00, 20 December 2005 (MST)--[[User:Ihabsraj|Ihabsraj]] 16:00, 20 December 2005 (MST)--[[User:Ihabsraj|Ihabsraj]] 16:00, 20 December 2005 (MST) 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 23:00, 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

--Ihabsraj 16:00, 20 December 2005 (MST)--Ihabsraj 16:00, 20 December 2005 (MST)--Ihabsraj 16:00, 20 December 2005 (MST)--Ihabsraj 16:00, 20 December 2005 (MST)

## 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