Advanced fluid mechanics
Graduate · Engineering
Syllabus focus
Standard syllabus · STEM / applied
Pricing
Graduate-level rates are set on consultation. See the pricing page for K–12 and undergraduate rates.
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
Notes
Topics reflect common engineering syllabi at US colleges and universities. Exact order, depth, and applied emphasis vary by institution, department, and instructor.