Computational fluid dynamics
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
Numerical methods for CFD
- Governing PDEs: continuity, momentum, energy
- Finite difference, volume, and element discretizations
- Consistency, stability, and convergence (Lax equivalence)
- CFL condition and time-stepping schemes
- Upwind versus central differencing for advection
- Pressure-velocity coupling: SIMPLE and PISO algorithms
- Staggered versus collocated grids
- Boundary conditions: inflow, outflow, walls
- Grid generation: structured, unstructured, hybrid
- Solution acceleration: multigrid and preconditioning
Turbulence and multiphysics CFD
- RANS, LES, and DNS hierarchy
- Turbulence model selection and wall functions
- Compressible flow solvers and shock capturing
- Multiphase flows: VOF and Eulerian-Eulerian methods
- Heat transfer and buoyancy in CFD
- Reacting flows and combustion models (survey)
- Fluid-structure interaction coupling schemes
- Adjoint-based shape optimization in CFD
- Uncertainty quantification in simulation
- Verification using method of manufactured solutions
STEM / applied
Software, HPC, and validation
- OpenFOAM, Fluent, or Star-CCM+ workflow labs
- Parallel decomposition and MPI scaling
- Post-processing: vorticity, Q-criterion, streamlines
- Wind tunnel and CFD validation case studies
- Automotive and aerospace external aerodynamics projects
- Internal flows: pumps, valves, and heat exchangers
- Atmospheric and environmental CFD applications
- Digital twin CFD for operating equipment
- Thesis-scale CFD research project
- Publication graphics and animation standards
Research frontiers
- GPU-accelerated CFD frameworks
- Machine learning turbulence closure models
- Lattice Boltzmann methods overview
- Blood flow patient-specific CFD
- Data assimilation with experimental measurements
- Exascale computing challenges
- CFD in additive manufacturing melt pools
- Conference paper presentation skills
- Peer review of CFD journal articles
- Qualifying exam CFD preparation
Notes
Topics reflect common engineering syllabi at US colleges and universities. Exact order, depth, and applied emphasis vary by institution, department, and instructor.