Exercises

1. Base Case – Unsteady Cylinder
   1. How many steps were there per lift coefficient oscillation once the oscillation reaches an apparently steady state? What do these oscillations represent physically?
   2. Why did you include the patched velocity found in the tutorial? What happens when you don’t include it in your calculated solution? Does anything change if you increase the patch velocity?
2. Varying Timestep - Unsteady Cylinder  
   1. Plot the Strouhal number: the dimensionless frequency oscillation (f*d/U) vs. the square of time step, and compare to the results in Fig. 5 of "Implicit Multigrid Computation of Unsteady Flows with Applications to Aeroelasticity" (Caughey 2001).
3. Altering Grid – Unsteady Cylinder
   1. Returning to a timestep of 0.2s, compare a mesh of 128 x 64 cells and a mesh of your choosing to the original mesh. Maintain the same cell height by altering the bias factor yourself.
   2. Once the solution is computed, calculate the lift oscillation frequency, and use Richardson extrapolation to compute the limiting frequency corresponding to zero mesh spacing (similarly to the procedure done in the paper by Caughey in part 2).
4. Altering Reynolds Number – Unsteady Cylinder
   1. Compare the results for Reynolds numbers of 60, 120, and 80 at a timestep of 0.2s and mesh 192x96. Create a graph of the Strouhal number (dimensionless frequency oscillation) as a function of these Reynolds numbers.

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