Neutron STEM Lab
Virtual engineering lab

Lid-Driven Cavity & Incompressible Flow

Solve 2D incompressible Navier–Stokes in a closed cavity and inspect velocity, streamfunction, vorticity, and convergence.

Fluid Mechanics / Numerical MethodsadvancedValidated educational model
Learning mode

Guided laboratory

Use the checklist when you want a structured lab. Explore mode leaves the instruments unrestricted.

Set up → solve → verify

Build your numerical experiment

Read the equations

Start with an example. Change one setting at a time and compare accuracy, conservation, and computation cost.

Boundary conditions. Top lid moves right; remaining walls have no slip. All walls are impermeable. Corner nodes are stationary.

Solver scales coordinates by L.
Positive speed along the top wall.
unitless
Sets viscosity ν = UL/Re; 2D laminar model.
unitless
Even count puts nodes on both centerlines; at most 65 × 65 nodes.
unitless
Stop earlier only when the steady-rate tolerance is reached.
unitless
Normalized interior rate; this does not establish mesh independence.

Choose an example or use the defaults, then run. Larger grids may take several seconds.

Keep this experiment

Valid settings are saved on this device. Project JSON preserves physical inputs and display units. Restore it and run again for fresh results.

Settings stay in this browser. Simulations run locally.

Measurements

Instrument readings

Horizontal velocity at center
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Recorded from the current completed simulation.
Normalized steady rate
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Recorded from the current completed simulation.
Theory

Equations and model

Incompressible Navier–Stokes

Streamfunction enforces incompressibility, while vorticity transport evolves the flow. The solver scales length by L, velocity by U, and time by L/U. Pressure is not reconstructed.

∂ω∂t+u∂ω∂x+v∂ω∂y=ν∇2ω\frac{\partial\omega}{\partial t}+u\frac{\partial\omega}{\partial x}+v\frac{\partial\omega}{\partial y}=\nu\nabla^2\omega−∇2ψ=ω,u=∂ψ∂y,v=−∂ψ∂x-\nabla^2\psi=\omega,\qquad u=\frac{\partial\psi}{\partial y},\quad v=-\frac{\partial\psi}{\partial x}Re=ULν,t∗=tUL\mathrm{Re}=\frac{UL}{\nu},\qquad t^*=\frac{tU}{L}

Walls, residuals, and mesh dependence

Streamfunction is zero on the closed walls. Thom wall vorticity approximates no slip. Stationary corners meet the moving lid in an idealized velocity jump. SOR solves the streamfunction equation at each time step. The normalized steady rate below uses dimensionless vorticity and time. Low residuals alone do not establish mesh accuracy.

ωtop=−2ψadjacenth2−2Uh\omega_{\mathrm{top}}=-\frac{2\psi_{\mathrm{adjacent}}}{h^2}-\frac{2U}{h}Rs=max⁡interior∣Δω∗/Δt∗∣max⁡(1,max⁡interior∣ω∗∣)R_s=\frac{\max_{\mathrm{interior}}|\Delta\omega^*/\Delta t^*|}{\max(1,\max_{\mathrm{interior}}|\omega^*|)}
Validation

Independent checks

Numerical balance or equation residualNot run

Review conservation, boundary, entropy, or residual checks.

Expected
—
Simulated
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Error
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Tolerance
0%

Run the experiment to perform this check.

Reference, bounds, or convergenceNot run

Review the specific check and its limits; this is not a universal accuracy certificate.

Expected
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Simulated
—
Error
—
Tolerance
0%

Run the experiment to perform this check.

Engineering interpretation

Run the experiment to generate an engineering interpretation.

Assumptions and limitations
Assumptions
  • Top lid moves right; remaining walls have no slip. All walls are impermeable. Corner nodes are stationary.
  • Constant properties; uniform one- or two-dimensional meshes.
  • Physical quantities stored in SI. Changing display units preserves the simulation.
Limitations
  • Educational numerical verification does not certify a physical design.
  • No arbitrary CAD geometry, turbulence, compressibility, multiphase flow, or free surfaces.
  • Grid resolution, bounded computation, and reference limits are reported explicitly.
Local experiment export

Save your measurements and setup

Exports are generated in your browser. No account or server upload is required.

Settings JSON
Current parameters and instrument controls, including waveform, output enable, scope coupling, timebase, trigger, and cursors when present. Data labs also include the dataset, mappings, exclusions, budget, or propagation setup.
Measurements CSV
Completed instrument readings with labels, units, and descriptions.
Plot PNG
The current canvas-based scope, transient, sweep, or statistics visualization when available.
Summary
Markdown report with objectives, setup, measurements, validation, interpretation, assumptions, and graded guided concept-check results.

Ready to export the current local experiment state.

Learning objectives

What this experiment should establish

  • Establish circulation.
  • Inspect the field.
  • Compare meshes.
  • Recognize a stop limit.
Check your understanding

Questions to answer from the experiment

  1. What drives the circulation?
  2. What does near-zero cell-flux divergence establish?
  3. What should be reported if maximum time is reached before steady tolerance?
  4. Why are upper corners mesh-sensitive?
Continue learning
CFD LaboratoryExplore the other numerical experiments.Fluid mechanics toolsConnect numerical results to fluid mechanics calculations.Data Analysis & Uncertainty LabAnalyze exported numerical data.

Sources and model review

Reviewed 2026-09-19. The educational model exposes its assumptions and validation; source references do not imply external certification.