Navier-Stokes equations: Difference between revisions

Latest revision as of 15:42, 17 June 2011

The incompressible Navier-Stokes equations are
$\rho {\frac {D\mathbf {u} }{Dt}}=-\nabla p+\rho \mathbf {g} +\mu \nabla ^{2}\mathbf {u} \,,$
$\nabla \cdot \mathbf {u} =0\,,$
for an adiabatic fluid. A prognostic equation for density is
${\frac {D\rho }{Dt}}=\kappa \nabla ^{2}\rho \,.$

@@ Line 1: / Line 1: @@
-The incompressible Navier-Stokes equations are
+The incompressible Navier-Stokes equations are <br>
 <math>
-\rho \left( \frac{\partial \mathbf{u}}{\partial t} + \left( \mathbf{u} \cdot \nabla \right) \mathbf{u} \right) = - \nabla p + \mu \nabla^2 \mathbf{u} \, ,
+\rho  \frac{D \mathbf{u}}{D t}  = - \nabla p + \rho \mathbf{g} + \mu \nabla^2 \mathbf{u} \, ,</math><br>
-</math>
+<math>
+\nabla \cdot \mathbf{u} = 0 \,, </math><br>
+for an adiabatic fluid. A prognostic equation for density is<br>
+<math>
+\frac{D \rho}{D t} = \kappa \nabla^2 \rho \, .
+</math> <br>

Navier-Stokes equations: Difference between revisions

Latest revision as of 15:42, 17 June 2011

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