Advanced fluid mechanics
Graduate · Engineering
Syllabus focus
Topics typically covered
Standard syllabus
Governing equations and exact solutions
- Navier-Stokes equations in vector form
- Vorticity transport and Kelvin's circulation theorem
- Boundary layer equations and similarity solutions
- Blasius and Falkner-Skan flows
- Momentum integral methods for boundary layers
- Transition to turbulence: linear stability intro
- Turbulent boundary layers and law of the wall
- Reynolds stress and closure problem
- Turbulence modeling: k-ε and k-ω overview
- Compressible flow: normal shock relations
Potential flow and external aerodynamics
- Velocity potential and stream function in 2D
- Superposition: source, sink, vortex, doublet
- Flow around cylinders and lift generation
- Thin airfoil theory and Kutta condition
- Panel methods for numerical lift calculation
- Drag breakdown: friction, pressure, induced
- High-lift devices and stall mechanisms
- Wind tunnel testing and similitude
- Hypersonic and rarefied flow awareness
- Multiphase flow fundamentals (survey)
STEM / applied
Turbomachinery and computational methods
- Axial and radial turbomachiner stage analysis
- Cavitation in pumps and propellers
- Computational fluid dynamics: discretization schemes
- Mesh generation for complex geometries
- Verification and validation for CFD codes
- Large eddy simulation versus RANS trade-offs
- Fluid-structure interaction coupling intro
- Microfluidics and low-Re devices
- Biofluid advanced models for arteries
- Research paper presentation on CFD application
Research and industry applications
- Aerospace propulsion internal flows
- Automotive aerodynamic optimization
- Offshore hydrodynamics and wave loading
- Atmospheric and oceanic circulation models
- Blood pump and ventricular assist device flows
- Additive manufacturing melt pool fluid dynamics
- Experimental methods: PIV and hot-wire anemometry
- High-performance computing for CFD
- Grant writing for fluids research proposals
- Qualifying exam fluids topic preparation
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Governing equations and exact solutions
Navier-Stokes equations in vector form
Coming soon - Potential flow and external aerodynamics
Velocity potential and stream function in 2D
Coming soon - Turbomachinery and computational methods
Axial and radial turbomachiner stage analysis
Coming soon - Research and industry applications
Aerospace propulsion internal flows
Coming soon
Notes
Topics reflect common engineering syllabi at US colleges and universities. Exact order, depth, and applied emphasis vary by institution, department, and instructor.