Definition
Plain language
A simulation technique built so that quantities that can't physically go negative — like pressure or density — never do, even when the math gets violent.
As stated in the literature
A property of numerical schemes guaranteeing that physically non-negative quantities (density, pressure) remain non-negative throughout a simulation; positivity-preserving limiters can conflict with adaptive mesh refinement, forcing pre-graded meshes.
Also called: positivity-preserving limiter, positivity-preserving scheme
Why it matters: Without it, a simulation can produce nonsensical negative values that cause the whole calculation to crash.
For example, in a simulation of air slamming against a fast capsule, this technique keeps the computed pressure from ever dropping below zero, which would be physically impossible.
Heard on the show
“So it picks a positivity-preserving subcell limiter.”Episode 042 — An Agentic Scientific Computing System That Actually Remembers What It Learns