Lab: Viscous flow

Material

1. Lecture notes: Section 5.3.

2. Template file from GitHub: template-report-Stokes.ipynb

Mandatory assignment (1p if submitted in time for deadline)

1. The domain

Change the computational domain into a channel with only one circular hole at the center of the channel.

2. The mesh  

Change the resolution of the mesh to a uniform mesh size of h=1/32. Then locally refine the mesh once in a circle of radius 1 centered at the circular hole. 

3. The inf-sup condition

Verify that the Taylor-Hood mixed element is stable, whereas equal order interpolation of the velocity and pressure is unstable. Describe how the instability manifests itself. 

Extra assignment (choose one: 1p if submitted in time for deadline)

4. Boundary conditions

Switch the  inflow and outflow boundaries so that the fluid flows from right to left. Describe how the pressure changes. 

5. Stabilization

Implement Brezzi-Pitkäranta stabilization and show that equal order interpolation is then stable.