Transient Navier–Stokes

Compute the time-dependent flow around a cylinder with the transient Navier–Stokes equation:

Here is the vector-valued velocity field, is the pressure and the identity matrix. and are the density and viscosity, respectively.

Set up parameters and a region.

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Visualize the region and the inflow profile.

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Out[2]=2

Specify the transient viscous Navier–Stokes equation with viscosity and density .

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Specify a function that ramps up the inflow velocity.

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Specify an inflow boundary condition on the left.

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Specify an outflow boundary condition on the right.

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Specify no-slip boundary conditions on the remaining walls.

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Replace parameters in the boundary conditions.

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Set up initial conditions such that the system is at rest.

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Time-integrate the Navier–Stokes equation on a mesh with specified spacing while interpolating the velocities with second order and the pressure with first order.

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Out[10]=10

Compute the vorticity of the flow field.

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Set up the color scheme to be used for the visualization.

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Visualize the vorticity.

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Out[13]=13

Generate the frames for an animation.

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More details about this model can be found in the documentation.