Advanced module

Computational Fluid Dynamics

Set up CFD with control volumes, meshes, boundary conditions, turbulence models, residuals, and validation data.

Course outline only for now. Full chapter-level lessons are still in progress. Use this page for readiness, concepts, worked-example format, practice, review, and portfolio direction. Complete course contents are live today for Math, Physics, and Statics.

01

Readiness check

Before starting, confirm the prerequisite habits.

  • Use Reynolds number.
  • Define boundary conditions.
  • Understand conservation of mass and momentum.
  • Know that mesh and model choices change results.
0 or 1 weak itemContinue, but slow down at the worked example.
2 weak itemsReview the foundation page linked in the roadmap before solving practice problems.
3 or more weak itemsStep back to prerequisites; this module depends on them.
02

The core idea

Run CFD as a controlled numerical experiment, not as a colorful picture generator.

CFD discretizes the flow domain and solves the Navier-Stokes equations numerically, but mesh quality, turbulence-model choice, and near-wall resolution decide whether the result is physics or numerical artifact.

Re = rho U D / mu
Works when: the mesh is refined where gradients are steep, the turbulence model fits the flow regime, and residuals plus a global balance confirm convergence.
Breaks down when: you read velocity contours off a coarse mesh with default turbulence settings and no convergence or boundary-condition check.
Figure 1. Concept model for Computational Fluid Dynamics. The figure names inputs, computed variables, geometry, and result.
input/load result/constraint computed variable dimension/model geometry
03

The method

1Model

Make the physical situation visible.

2Relate

Translate the model into symbols.

3Solve

Calculate only after the model is clear.

4Check

Use units, scale, and limiting cases.

04

Worked example

Figure 2. Worked problem setup: Air flows through a 0.15 m duct at 12 m/s. Estimate Reynolds number using rho = 1.2 kg/m^3 and mu = 1.8e-5 Pa s.
Figure 3. Calculation model. The result follows from the model, units, and reasonableness check.

Air flows through a 0.15 m duct at 12 m/s. Estimate Reynolds number using rho = 1.2 kg/m^3 and mu = 1.8e-5 Pa s.

  1. Problem Air flows through a 0.15 m duct at 12 m/s. Estimate Reynolds number using rho = 1.2 kg/m^3 and mu = 1.8e-5 Pa s.
  2. Given and find rho = 1.2 kg/m^3, U = 12 m/s, D = 0.15 m, mu = 1.8e-5 Pa s. Find: Reynolds number and likely flow regime.
  3. Assumptions Idealized model, consistent units, and no hidden effects outside the stated scope.
  4. Step Re = rho U D / mu.
  5. Step Re = 1.2*12*0.15/1.8e-5 = 120000.
  6. Step The flow is turbulent for an internal duct.
  7. Step Check CFD against pressure-drop data or a correlation.
  8. Conclusion Re = 120000, turbulent. Carry this result into the design decision, not just into the answer box.
05

Misconceptions and diagnostics

MistakeSymptomDiagnostic questionCorrection
Coarse-mesh confidenceReports values from an unconverged meshDid the result change on refinement?Run a mesh-independence study.
Wrong turbulence modelUses a model outside its valid regimeDoes the model fit this flow?Match the model (k-omega SST near walls) to the physics.
Ignoring near-wall resolutionWall treatment invalid for the meshIs the first cell height right for the wall model?Target y+ to the chosen wall function.
06

Practice ladder

Level 1: direct skill

Redo the worked example with one changed input. Predict the trend before calculating.

Check yourself

The trend must match the governing relation: Re = rho U D / mu.

Level 2: mixed concept

Draw the model from memory, label knowns and unknowns, then write the first equation without looking.

Check yourself

Your first equation should connect the model to pressure field.

Level 3: independent problem

Create a similar problem from a real object near you. State assumptions, solve it, and include a reasonableness check.

Check yourself

A valid solution has a sketch, given/find list, governing relation, units, and a conclusion.

Level 4: transfer task

Turn the result into a design decision: what would you change if the output missed its target by 25 percent?

Check yourself

Name the design variable with the strongest influence and justify it from the equation.

07

Working with AI, and proving it yourself

Useful AI role

Ask for a critique of assumptions, units, diagram labels, and missing checks after you have attempted the solution.

Do not outsource

Do not paste the problem and accept a final answer. Your evidence is the model, the checks, and the explanation.

08

Retrieval and spaced review

Closed-notes prompts: state which equations CFD solves, name the relevant Reynolds number, describe how you would check mesh independence, and say what y+ controls.

TodayRedo the worked example from a blank page.
+1 daySolve Level 1 without notes.
+3 daysSolve Level 2 with changed numbers.
+7 daysConnect this module to another course.
+30 daysAdd a portfolio artifact.
09

Mapping and portfolio task

Course mapping

CFD scales fluid mechanics the way FEM scales solids: the control-volume and dimensionless-number reasoning from fluids is exactly what tells you whether a CFD result is believable.

First-pass focus: definitions, model setup, units, and worked examples. Save edge cases for the second pass.

Portfolio task

Create a one-page CFD setup note (mesh, turbulence model, mesh-independence check): sketch, assumptions, equations, result, reasonableness check, limitation, and recommendation.