Computational Fluid Dynamics (EML4722)

Course Description

Computational Fluid Dynamics covers fluid kinematics, the differential formulation of conservation laws for fluid mechanics, numerical schemes for discretizing differential equations, turbulence models, and simulation of laminar and turbulent flows using modern tools.

Within the SCNS taxonomy, EML is the Mechanical Engineering prefix. The University of West Florida publishes this at 3 semester hours, prerequisite EML3016, giving approximately 45 contact hours.

CFD is the most powerful and the most dangerous tool a mechanical engineering undergraduate encounters. It will produce a beautifully rendered, entirely plausible, completely wrong answer without any indication that anything went wrong — and the industry has a genuine problem with practitioners who can drive the software and cannot judge the result. This course exists to produce the second kind of engineer, which is why it teaches the discretization and turbulence modelling underneath rather than only the interface.

Learning Outcomes

Required Outcomes

• Describe fluid kinematics and the material derivative.
• Derive the differential forms of conservation of mass, momentum, and energy.
• Describe the Navier-Stokes equations and the assumptions embedded in them.
• Classify partial differential equations and describe the implications for solution method.
• Describe finite difference, finite volume, and finite element discretization approaches.
• Apply Taylor series to derive finite difference approximations and determine order of accuracy.
• Apply the finite volume method and describe why it conserves.
• Describe explicit and implicit time integration and their stability characteristics.
• Analyze numerical stability and apply the CFL condition.
• Describe numerical diffusion and dispersion and their effect on solutions.
• Describe upwind, central, and higher-order convection schemes and their trade-offs.
• Describe pressure-velocity coupling and algorithms such as SIMPLE.
• Generate and evaluate computational meshes, including structured and unstructured types.
• Assess mesh quality and describe its effect on solution accuracy.
• Perform mesh refinement studies and demonstrate grid independence.
• Specify boundary conditions appropriately and describe their effect on the solution.
• Describe the physics of turbulence and the closure problem.
• Describe Reynolds-averaged turbulence models and their assumptions and limitations.
• Select a turbulence model appropriate to a flow and justify the choice.
• Describe wall treatment, y-plus, and near-wall meshing requirements.
• Describe large eddy simulation and direct numerical simulation and their cost.
• Assess convergence using residuals and monitored quantities.
• Verify and validate a simulation against analytical or experimental results.
• Post-process and present CFD results honestly and interpretably.

Optional Outcomes

• Describe compressible flow simulation and shock capturing.
• Describe multiphase and free-surface modelling.
• Describe conjugate heat transfer.
• Describe moving and deforming meshes.
• Describe high-performance and parallel computing for CFD.
• Complete an independent CFD project from geometry through validation.

Major Topics

Required Topics

• Fluid kinematics and the material derivative
• Differential conservation laws
• The Navier-Stokes equations
• PDE classification
• Discretization approaches
• Finite difference approximations and accuracy
• The finite volume method
• Explicit and implicit time integration
• Stability and the CFL condition
• Numerical diffusion and dispersion
• Convection schemes
• Pressure-velocity coupling
• Mesh generation
• Mesh quality
• Grid independence studies
• Boundary conditions
• Turbulence physics and the closure problem
• RANS turbulence models
• Turbulence model selection
• Wall treatment and y-plus
• LES and DNS
• Convergence assessment
• Verification and validation
• Post-processing and presentation

Optional Topics

• Compressible flow and shock capturing
• Multiphase and free surface
• Conjugate heat transfer
• Moving and deforming meshes
• Parallel computing
• Independent CFD project

Resources & Tools

• An Introduction to Computational Fluid Dynamics: The Finite Volume Method (Versteeg & Malalasekera) — the standard undergraduate text and the clearest treatment of finite volume.
• Computational Fluid Dynamics: The Basics with Applications (John Anderson) — excellent on the underlying physics and history.
• Numerical Heat Transfer and Fluid Flow (Patankar) — the classic; SIMPLE originates here.
• Turbulence Modeling for CFD (Wilcox) — the reference on turbulence closures.
• OpenFOAM — free and open source, industrial-strength, and increasingly used in industry; steep learning curve and genuinely worth it.
• ANSYS Fluent or CFX — the commercial standard; student versions are free with cell-count limits.
• SimScale — browser-based with a free academic tier.
• Python with NumPy and Matplotlib — free; writing your own one-dimensional solver from scratch is the single most valuable exercise in the course and takes an afternoon.
• NASA Turbulence Modeling Resource and the ERCOFTAC database — free validation cases with experimental data; the correct way to check a solver.
• ASME V&V 20 — the standard on verification and validation in computational fluid dynamics and heat transfer.

Career Pathways

• CFD engineer and analyst — a well-paid specialization; SOC 17-2141.
• Aerodynamics engineer — SOC 17-2011; Florida's aerospace sector and the Space Coast are a direct pathway.
• Thermal and cooling analyst — electronics cooling and data centre design are growing areas.
• HVAC and building simulation engineer — a large Florida sector.
• Turbomachinery engineer — Siemens Energy in Orlando.
• Automotive and motorsport aerodynamicist.
• Marine and naval hydrodynamics — Florida's shipyards and marine industry.
• Process and chemical engineering simulation.
• Coastal and environmental modelling — storm surge and dispersion modelling; see this repository's OCE3014C guide.
• Software development for simulation vendors.
• Graduate study — CFD is a common research entry point, and this course is genuine preparation.

Special Information

⚠⚠ CFD produces confident wrong answers — verification and validation are the discipline

• The software always produces a result, it is always rendered attractively, and nothing in the output distinguishes a converged, validated, physically meaningful solution from nonsense. That is the central professional hazard of the field.
• Verification asks whether you solved the equations right. Grid independence, order-of-accuracy checks, and comparison to analytical solutions address it.
• Validation asks whether you solved the right equations. Only comparison to experimental data answers it — and a simulation that has never been validated against measurement is a hypothesis, not a result.
• Always run a mesh refinement study. A solution that changes materially when the mesh is refined has not converged, and reporting it is reporting a mesh artefact.
• Residuals falling is necessary and not sufficient. Monitor a physical quantity you care about — a force, a mass flow, a temperature — and confirm it has stopped changing.
• Boundary conditions decide the answer. An inlet placed too close, an outlet with the wrong condition, or a symmetry plane where the flow is not symmetric will produce a confidently wrong solution.
• Sanity-check against hand calculation. Estimate the pressure drop, the drag, or the heat transfer analytically first — the same warning this repository applies to finite element analysis in the EML3011 and ETG3533C guides.
• Use the public validation cases. NASA's turbulence modelling resource and ERCOFTAC exist precisely so a solver can be checked against known answers, and using them is standard professional practice.

⚠⚠ Turbulence modelling is an approximation — and knowing which one is the skill

• Turbulence is not solved; it is modelled. Resolving all scales directly is computationally impossible for engineering flows, so every practical CFD result rests on a turbulence model that is an approximation with known failure modes.
• The closure problem is fundamental. Averaging the Navier-Stokes equations introduces unknown Reynolds stresses, and closing that system requires modelling assumptions rather than physics.
• Different models fail differently. k-epsilon is robust for free shear flows and poor near walls and in adverse pressure gradients; k-omega handles near-wall and adverse-gradient flows better and is sensitive to free-stream values; SST blends them and is the common default for separated flows; Spalart-Allmaras is cheap and well suited to attached aerodynamic flows.
• Separation prediction is where models most often fail — and separation is frequently the thing you are trying to predict.
• Wall treatment is not optional. Wall functions require a y-plus range; resolving the boundary layer requires a much finer near-wall mesh. Mixing the two incorrectly is one of the most common errors in student CFD.
• LES and DNS resolve more and cost far more. Knowing when the additional cost is justified is an engineering judgement about the decision the simulation supports.
• State the model and its limitations in any report. A CFD result presented without the turbulence model named is not a reportable result.
• Rule 11 applies — turbulence modelling is an active research area, and machine-learning-augmented closures are developing quickly.

⚠ Write your own solver — it is the fastest route to judgement

• Implementing a one-dimensional finite difference or finite volume solver takes an afternoon and teaches more about why simulations misbehave than a term of driving a commercial package.
• You will see numerical diffusion directly. A first-order upwind scheme smears a sharp front visibly, and understanding that this is the scheme rather than the physics is a permanent lesson.
• You will see instability directly. Violating the CFL condition produces oscillations that grow without bound, and watching it happen makes the stability analysis concrete.
• You will understand why higher-order schemes are not automatically better — they reduce diffusion and introduce dispersion and overshoot.
• You will appreciate what the commercial code is doing when it reports residuals, applies under-relaxation, or fails to converge.
• Verify against an analytical solution. One-dimensional conduction, Couette flow, and Poiseuille flow all have exact answers and are the standard first tests.
• Use version control and keep the code — it is portfolio material and it demonstrates something a certificate cannot.

⚠ An honest account of the workload

• Upper-division mechanical engineering demands sustained daily problem-solving. Budget eight to twelve hours a week outside class.
• Work problems without the solution visible. Reading a worked example produces the feeling of understanding and none of the ability.
• State your assumptions explicitly — knowing which assumptions apply is most of the subject.
• Carry units through every step and check that the answer is physically plausible.
• Go to office hours in week two, not week ten.

⚠ Institutional context — check the number against the description

• This guide is written from the University of West Florida catalog, which publishes a complete and explicit set of EML entries. Other Florida institutions teaching this subject may number it differently.
• The EML prefix is not consistent across Florida. This repository documents a genuine subject collision in the thermal-fluids sequence — EML3015 and EML3016 denote different subjects at UWF and at the FAMU-FSU College of Engineering.
• Much of the mechanical engineering core is also taught under the general engineering prefix EGN, and under SCNS those are different courses. Equivalency does not cross prefixes or a C or L suffix.
• Identify a course by its catalog description, never by its number or title, and give a receiving department the description rather than the number.

⚠ FE exam and PE licensure — this is the accredited engineering pathway

• This course sits inside an A.B.E.T.-EAC accredited engineering programme, the pathway that leads directly to professional licensure — distinct from engineering technology, where the route to a P.E. is longer.
• Florida licenses professional engineers under Chapter 471, Florida Statutes, through the Florida Board of Professional Engineers: A.B.E.T.-EAC degree → FE examination → qualifying experience → PE examination → licensure.
• The NCEES FE Reference Handbook is free and is the only reference permitted in the exam. Use it as your working reference now.
• Only a licensed P.E. may offer engineering services to the public in Florida, seal drawings, or use the title in a way implying licensure.
• Rule 11 applies — verify current requirements with FBPE and NCEES directly.

How Florida course levels affect transfer

The first digit of an SCNS number denotes the year of offering, not transferability. Courses at the 1000 and 2000 levels transfer transparently between Florida public institutions, and 3000 to 4000 is unproblematic since both are upper division. The boundary that actually matters is 2000 to 3000, where lower-division credit generally cannot satisfy an upper-division requirement.

EML4722 is 3 semester hours and approximately 45 contact hours. Expect a substantial simulation project alongside the theory, and expect out-of-class computation time to exceed the scheduled hours considerably.

Keep the project and document the verification and validation. A CFD study that includes a grid independence study, a turbulence model justification, and comparison to experimental or analytical data is genuinely persuasive in an interview — and it is exactly what distinguishes an engineer from a software operator.