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In this example, we will investigate the Poiseuille flow in a plain 2D channel. The objectives of this example is to introduce how to:
The Poiseuille flow is the fully developed laminar flow between two parallel plates induced by a constant pressure drop in a channel of length L. In general, the flow can be induced by any of the following way:
Here, the flow is induced by pressure boundary condition at inlet (west) and outlet (east) boundaries as shown in figure below.
The pressure drop along the channel per unit length is where,
The Reynolds number is defined as where, - the mean velocity. For the parabolic velocity profile, the mean velocity can be computed with .
The analytical velocity profile along channel height is given as the analytical pressure profile along the channel length is and wall shear stress profile along the channel height is The error between analytical solution () and simulated results () are defined by the relative error norm as
Here are the results from the simulation.
Velocity along the height of the channel:
Pressure across the length of the channel:
Wall shear stress along the height of the channel:
To create these plots, run python plot_track.py to create the plots. Before running the plot script, open 'plot_track.py' and update path to Gleaner script in 'glrPath'. Download Gleaner script using hg clone https://hg.osdn.net/view/apes/gleaner