Lab: Navier-Stokes equations

Material 

1. Lecture notes: section 5.4-5.5.

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

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

1. Reynolds number

Compute the Reynolds number based on the inflow velocity U and the diameter D of the cylinder. Compare simulations for Reynolds numbers Re = 1, 10, 100, 1000. For which Reynolds numbers is the flow unsteady and steady, respectively? 

2. Drag and lift coefficients

Compute the drag and lift coefficients Links to an external site., and the Strouhal number Links to an external site., for the cylinder at the different Reynolds numbers (Re = 1, 10, 100, 1000). Verify that the von Karman vortex street Links to an external site. has a Strouhal number of St≈0.2. 

3. Mesh resolution

Compare the solution for Re=100 under the different mesh resolutions h=1/8, 1/16, 1/32. Describe how the simulations change with respect to drag and lift coefficients and the Strouhal number. 

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

1. Stabilization

Modify the stabilization terms to the "Streamline diffusion" stabilization in the lecture notes section 5.5. Compare the solution at Re=100 with the previous stabilization, does the solution change for different mesh resolutions h=1/8, 1/16, 1/32? 

2. Benchmark

Modify the simulation problem to match the test case 2D-2 (unsteady) in the benchmark report by Schäfer and Turek.  Links to an external site.

3. Paraview visualization

Create movies of the simulation for Re=100 and h=1/32, by using the open source software Paraview Links to an external site.. To download the needed files, uncomment the following two lines in "template-report-Navier-Stokes.ipynb":