peclet-threshold

At its defaults it draws −εu″ + u′ = 0 on 31 points, ε = 0.005, cell péclet 3.125. Three solutions of a boundary-layer problem on the same grid. The exact one rises monotonically from 0 to 1 with a layer of width ε at the right-hand end. The central-difference answer alternates at every point and leaves [0, 1] at 16 of the 31 of them, by as much as 0.5152. The upwind answer is monotone at every Pe.

peclet-threshold is one function in lib/figures/convection.js — convection — the stencil that is not symmetric, and the fourier arguments that assumed it was. Everything below came out of it during this build, at arguments taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

Three solutions of a boundary-layer problem on the same grid. The exact one rises monotonically from 0 to 1 with a layer of width ε at the right-hand end. The central-difference answer alternates at every point and leaves [0, 1] at 16 of the 31 of them, by as much as 0.5152. The upwind answer is monotone at every Pe.

Three solutions of a boundary-layer problem on the same grid. The exact one rises monotonically from 0 to 1 with a layer of width ε at the right-hand end. The central-difference answer alternates at every point and leaves [0, 1] at 16 of the 31 of them, by as much as 0.5152. The upwind answer is monotone at every Pe.

Three solutions of a boundary-layer problem on the same grid. The exact one rises monotonically from 0 to 1 with a layer of width ε at the right-hand end. Below Pe = 1 the central-difference answer is monotone and inside [0, 1] like the exact one. The upwind answer is monotone at every Pe.

Every figure above asserted its own claims on the way to being drawn, and a claim that failed would have failed the build rather than drawn a wrong picture. Those assertions used to leave no trace at all: a passing one returned true and the only evidence the figure had checked anything was that nothing crashed. The list below is what they actually said, collected by running this generator with an observer installed — not a description of what it is believed to check.

10 distinct claims across 3 sets of arguments, grouped below by shape — because most of them are one sentence with a different number in it, and how many separate times that sentence was put to the test is the informative part.

It draws a decomposition and prints its residual. It calls solve, and every figure above carries the badge — which residualcheck verifies by looking for it in the emitted SVG rather than by finding the call that builds one. A badge that is constructed and then left out of the body is the failure that check exists for.

Across the library: the rule bites on 52 of 99 generators — 37 print a residual and 15 are exempt with a published reason; 47 factorise nothing. Read from lib/residual-rule.js, which is the same body the gate enforces from, and the gate's last check fails the build if this page and it disagree about any generator.