Neutron STEM Lab
Virtual engineering lab

Burgers Flow & Shock Formation

Solve nonlinear velocity transport, investigate shock formation, and track conservative fluxes and entropy decay.

Fluid Mechanics / Numerical MethodsintermediateValidated 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. Periodic velocity and conservative flux at both ends of the interval.

Physical length of the periodic domain.
unitless
Uniform cells; resolution increases both accuracy and computational cost.
Local characteristic speed equals local velocity.
Zero gives an exact constant-state check.
Zero removes physical diffusion; numerical diffusion may remain.
The last step lands at this physical time.
unitless
Automatic time steps use this fraction of the applicable explicit stability bound.

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

Mean-velocity balance error
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Recorded from the current completed simulation.
Final mathematical entropy
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Recorded from the current completed simulation.
Theory

Equations and model

Nonlinear conservative transport

Burgers flow isolates nonlinear steepening and diffusion. Its characteristic speed equals local velocity. Godunov selects the entropy-consistent Riemann flux; Rusanov adds local speed-dependent dissipation. This scalar equation is not a complete compressible gas model.

∂u∂t+∂∂x(u22)=ν∂2u∂x2\frac{\partial u}{\partial t}+\frac{\partial}{\partial x}\left(\frac{u^2}{2}\right)=\nu\frac{\partial^2u}{\partial x^2}FR=uL2+uR24−max⁡(∣uL∣,∣uR∣)2(uR−uL)F_{\mathrm R}=\frac{u_L^2+u_R^2}{4}-\frac{\max(|u_L|,|u_R|)}2(u_R-u_L)

Shock time and entropy

The smooth inviscid characteristic reference is used only before 80% of the sine-wave shock time. After that, or with nonconstant viscous flow, the lab withholds an exact error. The periodic mean is conserved; mathematical entropy cannot grow in the viscous or inviscid entropy solution.

u(x,t)=uˉ+Asin⁡[2πL(x−u(x,t)t)],ts=L2πA (A>0)u(x,t)=\bar u+A\sin\left[\frac{2\pi}{L}(x-u(x,t)t)\right],\qquad t_s=\frac{L}{2\pi A}\ (A>0)ddt∫0Lu22 dx=−ν∫0L(∂u∂x)2 dx≤0\frac{\mathrm d}{\mathrm dt}\int_0^L\frac{u^2}{2}\,\mathrm dx=-\nu\int_0^L\left(\frac{\partial u}{\partial x}\right)^2\,\mathrm dx\leq0
Validation

Independent checks

Numerical balance or equation residualNot run

Review conservation, boundary, entropy, or residual checks.

Expected
—
Simulated
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Error
—
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
—
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
  • Periodic velocity and conservative flux at both ends of the interval.
  • 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

  • Check the smooth reference.
  • Form a shock.
  • Compare flux schemes.
  • Test a limiting state.
Check your understanding

Questions to answer from the experiment

  1. Why does a Burgers sine wave steepen?
  2. What does increased viscosity do?
  3. Why withhold the smooth reference after shock formation?
  4. What does a conserved mean establish?
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.