WASHES · REFERENCE GALLERY · THE TEXTBOOK

Fluid Simulation for Computer Graphics

Robert Bridson, 2nd ed., 2015, AK Peters/CRC Press. The reference for everything in the Washes fluid pipeline, especially the advection chapters behind the v0.67–v0.72 work.

Bridson's advection chapter is a catalog of tradeoffs, and this bench runs three of its entries head to head: the same sharp-edged block of pigment, the same diagonal drift on a wrapping domain, the same Δt. Donor-cell upwind is first-order, conditionally stable, and diffusive. Semi-Lagrangian is unconditionally stable but smears just as much. MacCormack (the unconditionally stable variant: advect forward, advect back, correct by half the round-trip error, then clamp to the local interpolation bounds) recovers second-order accuracy and keeps edges crisp.

The sharpness number under each panel is the field's steepest edge gradient as a fraction of its initial value — a direct measure of how much edge contrast each scheme has destroyed.

CFL = 1
0.90
Donor-cell — 1st order, CFL-bound sharpness 100% · min 0.00
Semi-Lagrangian — stable, diffusive sharpness 100% · min 0.00
MacCormack — stable, 2nd order, clamped sharpness 100% · min 0.00

Try this

1. Run at Δt = 0.90 for thirty seconds and compare sharpness numbers. Donor-cell and semi-Lagrangian decay together toward mush; MacCormack diffuses too, but holds roughly three times their edge contrast indefinitely. Same stencil cost class, visibly different result — the error-compensation trick is nearly free.

2. Push past CFL = 1. Donor-cell disintegrates into negative-pigment noise; both backtracing schemes sail on. The two failure axes — stability and diffusion — are independent, and MacCormack is the corner of the chart that wins both.

3. Watch MacCormack's block corners closely at large Δt. The clamp is what keeps them from ringing with over- and undershoot; the unclamped corrector would oscillate at sharp edges. Bridson covers exactly this failure mode — it's why Washes v0.72 shipped the clamped variant.

This page benches the advection chapter only. The book's other half of the Washes pipeline — the pressure projection that keeps the velocity field divergence-free — is demonstrated on the Foster & Metaxas page via the staggered-grid null-mode experiment.