On completion of this module students should be able to
1. Write down the eigenvalue problem for the canonical physical systems of
Fluid Dynamics
2. Derive the Orr--Sommerfeld equation and compute exact solutions in
certain cases
3. Describe the subtle features of linear stability theory beyond temporal
eigenvalue analysis
4. Carry out a Stuart--Landau analysis on simple nonlinear equations
5. Characterize turbulence using the Kolmogorov and Reynolds-averaged
theories.
6. Solve sparse linear problems iteratively and implement their solution
in a programming language of the student's choice.

In addition to the study of sparse linear systems and their role in
Computational Fluid Dynamics, a number of mini-projects will form part of
this module. Therefore, on completion of this module students should gain
much familiarity with computational methods in fluids. In particular,
students should further be able to

1. Perform an Orr--Sommerfeld stability analysis of Poiseuille flow using
spectral methods in Matlab
2. Solve nonlinear wave equations numerically to test for the
applicability of Stuart--Landau theory
3. Implement an existing parallel flow solver (S-TPLS) to study large-eddy
simulations in turbulent channel flow
4. Analyse the turbulent statistics emanating from the simulations under
item (3) above.

MSc / PhD level module. Students are therefore expected to have completed prior modules in Complex Analysis and Partial Differential Equations, at least two prior modules in Fluid Dynamics, and at least one prior module in Computational Science with significant programming content

• Feedback individually to students, on an activity or draft prior to summative assessment

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