Rheon

SIX MECHANISMS

Read. Predict. Compare.

Each example isolates one question. Scrolling selects a saved reference state; controls let you test the comparison. No example advances a live fluid solver.

01 / 06

Pressure removes incompatible flux

Compare the original face field with the complete pressure correction. Cell markers show incidence; arrows keep the same speed scale.

Predict, then compare

At 100%, maximum incidence approaches the stored solve residual and the unit-weight kinetic norm falls. At 50%, incidence is approximately half its starting value.

Scope. The slider blends two saved fields. It is not a PCG iteration history or a moving-wall solve. The incidence has graph units, not physical divergence in s⁻¹.

Read the derivation →

02 / 06

Find the first crossing

Select a crossing, a near miss and an inside start. The orange marker is the earliest triangle intersection along the finite segment.

Predict, then compare

A crossing can start and end outside yet still have a hit with 0 ≤ t ≤ 1. A near miss reports no intersection.

Scope. These are static translated mesh poses with query tolerance 10⁻¹². The wall-speed arrow is prescribed metadata; no moving-boundary interval is solved. The Lean claim is for an infinite stationary plane.

Read the derivation →

03 / 06

Density changes the pressure gradient

Compare two half-metre layers at rest. All cases use one pressure-arrow scale, so a larger bottom pressure makes a longer arrow.

Predict, then compare

Bottom gauge pressure equals 9.81 × (ρlower / 2 + ρupper / 2) Pa. Compare the measured readout with this independent formula.

Scope. The reported face balance error checks the discrete increments against a piecewise analytic oracle. No interface transport or stratification evolution is computed.

Read the derivation →

04 / 06

Measure damping, not just motion

Choose viscosity and a saved time. Velocity arrows retain one scale; increasing time damps the periodic sine mode.

Predict, then compare

Energy decreases. Compare the dense implicit result with the discrete eigenmode and inspect the gap from continuum decay.

Scope. This is a scalar periodic shear reference extruded into 3D. The amplitude gap is a discretization effect, not a certified error bound for a general tensor or free-surface solver.

Read the derivation →

05 / 06

Separate fluid slip from wall motion

Keep the lower wall stationary and the upper wall at 1 m/s. Increase only the lower Navier slip length.

Predict, then compare

Fluid slip speed rises while wall shear falls. The lower wall itself remains at 0 m/s; the upper wall remains no-slip.

Scope. The analytic steady Couette model has one slipping wall. It does not stand in for the separately recorded two-wall, transient or forced native cases.

Read the derivation →

06 / 06

Separate wetting shape from tension

At fixed volume, vary contact angle to change contact radius. Then hold the angle fixed and change surface tension.

Predict, then compare

Tension changes pressure jump and adhesion work, while radius and volume stay fixed. The volume integral error measures quadrature agreement.

Scope. A spherical cap is a zero-gravity equilibrium oracle. It does not demonstrate relaxation, hysteresis, contact-line dynamics or stable liquid stepping.

Read the derivation →

Continue with recomputed mechanisms

Sampling and transport: inspect lattice offsets, overshoot and the limits of fallback.

Continue with qualified native records

Wall and force sequence · Obstacle pressure and reduced shear · Finite strain. Each page states whether its required qualified packet is included.

Chapter introduction

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