# Poisueille flow in a channel 2D

In this example, we will investigate the Poiseuille flow in a plain 2D channel. The objectives of this example is to introduce how to:

• Create a mesh with boundaries using Seeder.
• Post-process the mesh using Seeder-harvester and visualize it Paraview.
• Simulate Poiseillie flow in the channel using Musubi.
• Validate the numerical results.
• Visualize the flow in Paraview.
• Create a 2D plot using Gleaner tool. Gleaner is a Python tool which extracts data from Musubi ascii output and uses matplotlib in python library to create a plot.

## Problem description

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:

• Defining pressure at inlet and outlet of the channel.
• Defining velocity at inlet and pressure at outlet of the channel. Here is the example.
• Using pressure gradient i.e. pressure drop/length as a external force. Here is the example.

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,

• $\mathbf{U}_m$ - the maximum fluid velocity at the channel center axis,
• $\rho=1.0$ - the fluid density and
• $\nu=10^{-3} m^2/s$ - kinematic viscosity.

The Reynolds number is defined as where, $\bar{U}$ - the mean velocity. For the parabolic velocity profile, the mean velocity can be computed with $\mathbf{\bar U} = 2 \mathbf{U}_m /3$.

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 ($u_a$) and simulated results ($u_s$) are defined by the $L^2$ relative error norm as

## Post-processing

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

Musubi was developed by University of Siegen