Periodic sine diffusion
Expected: RMS reference error below 0.02%; conserved integral
Observed: 0.0018173% error; 1.48e-14% balance
passComputational Fluid Dynamics Laboratory
Watch a pulse travel, follow viscous startup, stir a dye spot, or solve circulation inside a cavity. Then examine how the numerical evidence supports the result.
No account or installation. Calculations run in your browser. Save portable projects and export numerical data when you need it.
Choose an experiment
Begin with a worked example. Guided mode adds procedures and graded concept questions; exploration mode leaves you free to investigate.
Advection, Diffusion & Numerical Error
Transport a periodic scalar, compare upwind and Lax–Wendroff schemes, and distinguish physical diffusion from numerical smearing.
Burgers Flow & Shock Formation
Solve nonlinear velocity transport, investigate shock formation, and track conservative fluxes and entropy decay.
Transient Couette–Poiseuille Flow
Resolve viscous channel startup with an implicit momentum solver and compare against transient and steady analytical profiles.
2D Dye Transport & Conservation
Advect and diffuse dye in a prescribed divergence-free velocity field, inspect snapshots, and check scalar conservation.
Lid-Driven Cavity & Incompressible Flow
Solve 2D incompressible Navier–Stokes in a closed cavity and inspect velocity, streamfunction, vorticity, and convergence.
Mesh Refinement & Solver Verification
Solve a manufactured 2D Poisson problem on three nested meshes and compare exact error, residuals, observed order, and GCI.
A smooth picture is only the beginning
Stability keeps a computation from growing uncontrollably. Conservation checks a balance. A residual measures how closely the discrete equations have been solved. None alone proves that the mesh resolves the solution.
Use analytical transport and channel references, then refine the grid. In the manufactured Poisson experiment the exact solution is known in advance: watch iterative error and spatial error behave differently.
Inspect the evidence
Field maps include fixed color limits across saved times, velocity arrows where applicable, and a coordinate inspector accessible by keyboard. Profiles, histories, and tables preserve the final numerical results. CSV exports retain calculation precision.
Runs use background computation when supported. Cancel at any time or edit the setup to stop it. Cancelled runs provide no completed measurements. A completed calculation that reaches a time or work limit preserves its convergence warning.
Numerical verification6/6 published reference checks passReviewed 2026-09-19
View numerical reference cases
Constant Burgers state
Expected: Exact preservation
Observed: 0% error
passTransient channel series
Expected: RMS error below 1% of reference scale
Observed: 0.096592%
passPeriodic 2D scalar balance
Expected: Integral conserved within 10⁻⁹%
Observed: 0.00%
passManufactured Poisson solution
Expected: Order 1.95–2.1; relative residual below 10⁻⁹
Observed: Order 2.0104; residual 5.15e-10
passNASA three-grid arithmetic
Expected: Order 1.78617; GCI 0.103083%
Observed: Order 1.78617; GCI 0.103083%
passSource tests also verify the cavity transport operator against a manufactured two-mode solution, plus wall conditions and flux closure. A passed implementation check does not establish physical or mesh accuracy for every input.
Model scope and limits
The cavity solves two-dimensional incompressible laminar Navier–Stokes in streamfunction–vorticity form for Reynolds numbers 10–400. Dye uses prescribed velocity; channel flow assumes fully developed conditions; Burgers flow is a scalar nonlinear conservation model.
These bounded educational solvers exclude arbitrary CAD meshes, turbulence models, compressible gas dynamics, multiphase flow, and free surfaces. Each experiment exposes its boundary conditions, references, and stopping limits.
Continue with fluid mechanics tools or use the Data Analysis & Uncertainty Lab to inspect exported data.