What it shows
A standard textbook problem describes a liquid turning to vapour, with the boundary between the two moving over time. It has an exact answer, so the right position of the boundary is known at every moment. The problem and the solver both come from the solver’s authors, not from us.
We ran the solver and compared its boundary with the exact answer at every recorded time after a short start-up period:
- The worst difference was 1.43%.
- The pass bar was 5%, written down before the comparison was computed.
- Over 6,111 comparison points, the typical difference was 1.08%.
So the solver reproduces this one-dimensional evaporation problem well inside the bar we set.
Why it matters
A coolant designed by computer is only as good as the simulations behind it. Here a simulation tool we use met a known answer, under a bar written down before the comparison was computed. The solver output it graded already existed when the bar was written, and the problem is its authors’ own, so this is not a blind test.
It is also narrow. It shows the phase-change solver handles a moving liquid-vapour boundary. It says nothing about the flow that differences in surface tension would drive, and the heat-flux figures elsewhere on this site come from a separate model that this check does not test.
Who should care
- Engineers who qualify two-phase cooling and want to know which parts of a simulation stack have been checked against an exact answer.
- A lab or partner deciding whether our simulations are a sound place to start bench work.
- An investor sorting checked results from modelled ones. This one is checked; it is a check of a tool, not of a fluid.
The post on how we check a simulation sets this result beside the two comparisons that missed.
The limits, in the lab’s own words
Quoted word for word from the published file named under each quote. Read the result with them.
this is not a test of the solver on any FluxZero fluid. The three blend runs in the same record reuse this one-dimensional setup with each blend's density and viscosity and a constant surface tension, so they contain no surface-tension-driven flow and are not evidence of it. No FluxZero fluid has been mixed or measured.
From The boiling solver’s grade on the exact textbook problem.
it also records that the boiling-solver check reads a solver output that is not committed, so it cannot rerun from a fresh copy of the repository.
From The lab’s record of its checks, read from its results file.
The pass bar and the comparison window were written down on 2026-09-23, before the comparison was computed
From The boiling solver’s grade on the exact textbook problem.
Prior art
The published work this result uses or is checked against. Each link was opened and checked when this page was written.
- boilingFoam, the open-source boiling solver and its benchmark cases (GitHub): the solver we ran and the Stefan problem case it ships with, both its authors’ work, not ours
- The Stefan problem (Wikipedia): the classic moving-boundary problem of a phase change, which has a closed-form answer
Evidence
Each number with a dotted underline was read from one of these published files, field by field, when this page was built.