∿NS-B Experiment Lab

A COMPUTATIONAL FLOW EXPERIMENT

Watch the flow.
Measure the uncertainty.

Run a real numerical Navier–Stokes calculation. Change its resolution, inspect the evolving field, and compare explicit error bounds for four saved reference trajectories.

Research by Rushikesh Murlidhar Walke

02Explore the calculated flowREFERENCE

A slice through a 3D flow

z = π/4

Arrows show the x–y velocity. Colour shows velocity through the slice, u_z. All three velocity components are calculated.

yxt = 0.00000
Loading the reference data…
−uz+uzFixed colour scale
0.00000 / 0.25

Playback advances through calculated endpoints; the arrows are a numerical visualisation, not a proof.

03Inspect the error bound
ARCHIVED RATIONAL REFERENCE ONLY
≤—

Normalized spatial L² velocity error
(root-mean-square vector velocity error)

t = 0

The bound compares the saved rational reference with any Leray–Hopf energy solution of this initial-value problem, under the setting and reconstruction specified in the certificate.

What is included in this bound?

The certificate uses exact rational full-residual calculations for the saved reconstruction, including modes outside the solver cutoff, with a standard energy-stability estimate.

This is a finite-time spatial L² estimate. It is not a pointwise error, percentage error, or general global-regularity result. The paper’s X-norm claim is a separate statement.

Read the mathematical method ↗

A bound through time

—

Each step uses the following endpoint’s bound throughout its interval. Select a saved time to inspect its endpoint bound.

Upper bound for the archived rational reference

Displayed bounds are rounded upward. Graphs and ratios use approximate decimals; the downloadable report contains exact certificate values and derivation.

MAKE REFINEMENT VISIBLE

Four calculations. One common test.

Compare final-time upper bounds at t = 0.25. A smaller bound gives a tighter guarantee for that saved trajectory.

ResolutionTime stepModesFinal error boundInspect

This comparison evaluates these four reference calculations. It does not establish an advantage over another CFD package or a new industrial application.

A CONCRETE TECHNICAL STEP

A flow calculation with inspectable uncertainty.

Use this benchmark to examine the gap between a numerical approximation and an explicit mathematical guarantee. The solver, residual calculation and reports are available for inspection and reproduction.

The certificate here uses a standard energy-stability argument. It does not yet demonstrate a performance or accuracy benefit from the preprint’s novel theorem. Industrial validation and independent review remain future work.