Solution of Navier-Stokes equations

(Difference between revisions)

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:

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 For the incompressible flows, the Navier-Stokes equation could be written in the form: <br>
 :<math>
-\nabla  \bullet \vec U = 0 </math> <br>
+\nabla  \cdot \vec U = 0 </math> <br>
-:<math> {{\partial \vec U} \over {\partial t}} + \nabla  \bullet \left( {\vec U\vec U} \right) -  \nabla  \bullet \left( {\nu \nabla \vec U} \right) =  - \nabla p </math>
+:<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>