Vortex Flow

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Model Data

Type: fluid dynamics

Physics Modes: navier stokes equations

Keywords: validation

Time dependent decaying flow for standing vortices with the following analytical solution to the Navier-Stokes equations

\[ \begin{array}{l} u = -cos(kx) sin(ky) e^{-2\nu k^2t} \\\
v = sin(kx) cos(ky) e^{-2\nu k^2 t} \\\
p = -\frac{1}{4}(cos(2kx)+cos(2ky)) e^{-4\nu k^2 t} \end{array} \]

The two-dimensional flow problem is solved for a unit square with k = 2π and the exact solution as boundary and initial conditions.

This model is available as an automated tutorial by selecting Model Examples and Tutorials… > Fluid Dynamics > Vortex Flow from the File menu. Or alternatively, follow the linked step-by-step instructions.

FEATool Multiphysics Tutorial - Vortex Flow