From the Navier-Stokes equations to the wave equation. Fundamental aeroacoustic sources. Applications in jet and airframe noise. Lighthill's and Curle's acoustic analogies. The Ffowcs Williams and Hawkings equation and its applications including solid and permeable surfaces. Amiet's theory and Ffowcs Williams and Hall analogy for trailing-edge noise. Sound scattering in porous materials and elastic media. Numerical methods for aeroacoustics. Boundary integral equations.
Finite difference and finite volume methods. Dispersive and dissipative properties of numerical schemes. High-resolution schemes. The Riemann problem and shock capturing schemes. Explicit and implicit time-marching schemes and the method of lines. Analysis of stability of numerical schemes. Structured and unstructured grids. Compact schemes, ENO and WENO schemes. Algorithms for the solution of the Euler and Navier Stokes equations.
The fundamental equations of fluid mechanics. Invariance properties of the Navier Stokes equations. Fundamentals of statistics including applications in turbulent flows. Reynolds decomposition and Reynolds stresses. Free turbulent flows. Turbulent flows in the presence of walls. Turbulent kinetic energy, production, dissipation and transport. Turbulent scales and spectra. Turbulence anisotropy. Large eddy simulation and direct numerical simulation. Fundamentals of turbulence modeling. Compressibility effects. Coherent structures and proper orthogonal decomposition.
Definitions of stability. Method of normal modes. Thermal instability. Inviscid stability of parallel flows. The Orr-Sommerfeld and Squire equations and Squire's theorem. Viscous effects. Adjoint problem and bi-orthogonality. Transition to turbulence. Non-modal analysis and transient growth. Resolvent operator and input-output analysis. Dynamic mode decomposition. State-space design and fundamentals of linear control. Controllability and observability. Extremum seeking. Model predictive control and neural network control.