u/AllAboutCFD

They remain one of the best collections of Fluid Mechanics videos I have ever come across, absolutely worth watching!

I haven’t seen a better visual resource that explains the fundamentals of fluid mechanics so effectively!

Created nearly half a century ago under the direction of the National Committee for Fluid Mechanics Films, these videos brilliantly cover almost all fundamental fluid flow phenomena.

What makes them stand out is how heavily they are illustrated with real experimental visuals.

Just google "National Committee for Fluid Mechanics Films (NCFMF)" to find these lectures.

If you are new to CFD or aiming to strengthen your fundamentals and move to advanced topics, the Ansys Learning Center is a valuable resource to explore.

Along with free foundational courses on Fluid Dynamics and Ansys Fluent, it also offers advanced CFD topics, such as:
• Turbulence Modeling
• Multiphase Flow
• Transient Simulations
• Conjugate Heat Transfer (CHT)
• And many more application-oriented modules

Most courses are 2–4 hours long, well structured, and some include completion certificates, making them useful for students, beginners, and working professionals.

Just google 'ANSYS Innovation Space", you will easily find these resources.

3 weeks series free course on openFOAM!

This series gives the possibility of getting a more detailed understanding of the basics of OpenFOAM.

It can be completed in about three weeks.

▶ Week - 1
openFOAM Installation
Introduction to openFOAM
Theory & Fun simulations

▶ Week - 2
Geometry preparation & Meshing
Turbulence Modeling
Multiphase Modeling
Parallelization in openFOAM

▶ Week - 3
Programming in openFOAM

Just google, "3 weeks series openfoam" you can find it easily.

Check out this amazing series. It's free!

3 weeks series free course on openFOAM!

This series gives the possibility of getting a more detailed understanding of the basics of OpenFOAM.

It can be completed in about three weeks.

▶ Week - 1
openFOAM Installation
Introduction to openFOAM
Theory & Fun simulations

▶ Week - 2
Geometry preparation & Meshing
Turbulence Modeling
Multiphase Modeling
Parallelization in openFOAM

▶ Week - 3
Programming in openFOAM

Just google, "3 weeks series openfoam" you can find it easily.

Check out this amazing series. It's free!

At the top, we have DNS, the most expensive one. It is not a turbulence model at all.

In the DNS, we solve instantaneous Navier-Stokes equations numerically without any turbulence model.

Then we have LES, which is less expensive than DNS but very often still too expensive for practical application.

In LES, large eddies are directly resolved, and smaller ones are modeled.

We put a filter that comes from a mesh resolution, above which turbulence eddies are resolved.

In RANS, we use Reynolds averaging, through which we average out all the information on turbulence.

We have to use the Turbulence Model along with the RANS equation to close the system, and it accounts for the effect of turbulence in the average flow.

That is the challenge and the art of turbulence, then.

We have the Reynolds Stress Model, which is a bit expensive but gives a more realistic picture of turbulence.

In RSM, we solve the transport equation for each of the Reynolds stress components, allowing us to capture the effect of anisotropy.

2 Equation Eddy viscosity models, the running horse of industries, are the least expensive ones where we apply the Boussinesq hypothesis.

Reynolds Stress is related to the mean velocity gradient; there is a linear relationship between stress and strain.

The wall function uses an empirical formula formulated based on experimental measurements and documented as the "Law of the Wall"

That empirical formula satisfies the log-region velocity profile.

So, you have to put the first cell centroid in the log layer.

In the second-order finite volume method, the variation across the cell for any flow variable is linear.

You are not resolving the velocity gradient as first cell placed in the log layer, but the wall shear stress must be correct.

The wall function modifies the viscosity in the cell adjacent to wall such that the product of velocity gradient and viscosity, shear stress, remains correct.

We will have wall functions computed near the wall for other flow quantities.

The thickness of the log layer plays a critical role in the selection of the wall function.

Wall Function should not be used for the flows prone to separation.

In resolved boundary layer approach, mesh up-to the viscous sub layer is resolved such that the first cell centroid lies within the viscous sublayer.

This allows direct resolution of the velocity and turbulence gradients in this thin layer, instead of relying on wall functions.

In resolved boundary layer approach, Low-Re models are often used.

Low-Re turbulence models is a modified version of a traditional turbulence model (like k-ε or k-ω).

There are additional source terms in the turbulence equations to control how turbulence is suppressed near the wall.

These extra terms or functions account the effects of viscosity near the wall.

Different models use different damping functions​ which are dependent on local Reynolds numbers and vanish near the wall to suppress turbulence there.

Convergence of "resolved boundary layer approach" can be very slow because of high aspect ratio cells near the wall and very high overall mesh count.

Image Source: "Computational Modelling of Non-Equilibrium Condensing Steam Flows In Low-Pressure Steam Turbines 0.1016/j.rineng.2019.100065 Ahmed M. Nagib Elmekawy, Mohey Eldeen H.H. Ali"

CFD Fundamental Theory Notes!

Structured, concise, well-organized, and easy-to-follow set of CFD notes with Python codes.

20 Modules Lecture Notes PDFs on the following topics:

🔹Introduction to CFD & Fluid Mechanics
🔹Overall CFD Workflow & Governing Equations
🔹PDEs & Discretization
🔹Finite Difference & Finite Volume Method
🔹Python coding: Diffusion & Convection-Diffusion
🔹SIMPLE Algorithm
🔹Mesh Generation, Mesh Quality & Accuracy in CFD
🔹Turbulent Flow Theory
🔹K-Epsilon Model: Standard, RNG & Realizable
🔹K-Omega Model: Wilcox, BSL & SST

Link to resources to mentioned in the comment/conservation section.

This material is designed for those who prefer structured, ready-to-use CFD learning notes. More than 400 learners have already enrolled in this CFD Learning Material!

If you want to learn how to code CFD, you have to start with this!

Step by Step 12 python module to write your own 2D Navier-Stokes finite-difference solver from scratch.

1️⃣ 1D Linear Convection
2️⃣ 1D Non-Linear Convection
3️⃣ 1D Diffusion Equation
4️⃣ 1D Burger's Equation
5️⃣ 2D Linear Convection
6️⃣ 2D Non-Linear Convection
7️⃣ 2D Diffusion Equation
8️⃣ 2D Burger's Equation
9️⃣ 2D Laplace Equation
1️⃣0️⃣ 2D Poisson Equation
1️⃣1️⃣ 2D Cavity Flow
1️⃣2️⃣ 2D Channel Flow

Just google "12 Steps to Navier Stokes" to find these modules!

One of the most interesting things in CFD and Fluid Mechanics is how the physics of flow changes with PDE classification.

• Elliptic PDEs → equilibrium & potential flow problems
• Parabolic PDEs → diffusion and dissipative transport
• Hyperbolic PDEs → wave propagation, shocks, compressible flow

Each equation type has completely different mathematical behavior, boundary conditions, and solution characteristics.

CFD Roadmap + AI/ML Roadmap + CFD Theory Material

If you are starting your journey in Computational Fluid Dynamics, understanding the CFD process flow is the first big step.

This simple diagram breaks it into 6 clear stages:

1️⃣ Geometry – Define your model and domain
2️⃣ Physics – Select flow solver, Set fluid properties, BCs & ICs
3️⃣ Mesh – Create structured/unstructured grids
4️⃣ Solve – Run simulations with the right numerical schemes & convergence criteria.
5️⃣ Reports – Verify, validate, and analyze numerical outputs
6️⃣ Post-Processing – Visualize results with contours, vectors & streamlines

Once you understand this roadmap, you will know where each skill, course, and tool fits in the bigger picture.

CFD Roadmap + AI/ML Roadmap + CFD Theory Material: https://topmate.io/all_about_cfd/1803822

CFD postprocessing is storytelling!

When we run CFD, the solver gives us numbers, contours, and vectors.

But those plots alone rarely convince anyone.

At the end of the day, CFD doesn’t sell itself.

The story you tell through your postprocessing does.

When I look back at my early CFD projects, I realize something important.

I thought running the solver was the hardest part.

Mesh generation, turbulence models, BCs, I obsessed over them.

When the results came in, I proudly shared contour plots and vector fields.

And the response was silence.

Why? Because nobody else in the room could see what I was seeing.

To them, it was just a rainbow of colors.

To me, it was flow separation, pressure recovery, and efficiency losses.

That’s when I understood, post processing is not plotting. It’s storytelling.

The job of a CFD engineer is not just to simulate. It’s to translate.

To take terabytes of raw data and weave them into a story that drives action.

Anyone can generate plots.

But only an engineer who can tell the story can create impact.

Source: SimScale [Vorticity at the back of the estateback DrivAer model]

Video

A US Navy fighter jet creating “shockwave lines” as it approaches close to the speed of sound.

Actually, the airplane is going slightly less than the speed of sound.

but as the air passes over various parts of the wings and fuselage, it can accelerate to supersonic speeds.

As this happens, the air will be compressed or expanded and those changes in pressure will change how light is refracted or bent as it passes through.

The visible effect is those ‘shockwave’ lines, or sometimes a cone-shaped cloud that envelops part of the aircraft if the air is humid enough.

Physics seen in reality. How beautiful this photo is.

Photo shot by Camden Thrasher.

Fluid dynamics looks complex… it is just one equation at its core!

➡️ Navier–Stokes Equations
The most general equation that governs how fluids move.

➡️ Euler Equations
High speed fluid motion when we ignore viscosity (no friction effects).

➡️ Stokes Equations
Very slow flow where inertia is negligible and viscous effects dominate.

➡️ Hydrostatic Equation
Pressure variation in a fluid that is completely at rest under gravity.

Based on dominant physics, these are simplified forms of Navier-Stokes.

Different numerical methods solving same fluid & heat flow physics.

All of these methods aim to solve the same governing equations (mass, momentum, and energy conservation) but from very different perspectives:

FDM: approximates derivatives directly on structured grids using Taylor Series.

FVM: enforces conservation locally over control volumes (industry favorite).

FEM: uses variational formulation & shape functions (strong in solid–fluid coupling).

LBM: mesoscopic approach using particle distribution functions & Boltzmann equation.

SPH: Mesh free Lagrangian, particle-based method for highly deforming flows.

The physics doesn’t change but the mathematics and discretization philosophy do.

As CFD engineers, understanding why a method works is far more important than just knowing how to run a solver.