Limit tracers

Spectral-element transport overshoots: a tracer bounded between 0 and 1 develops values outside that range where the flow is under-resolved. ClimaCore.Limiters provides a horizontal quasi-monotone limiter that restores element-local bounds while conserving mass, and a vertical mass borrowing limiter that removes negative values. Both are applied to the state after a time step or stage.

Quasi-monotone limiter (horizontal)

The limiter of [14] solves, in each element, the constrained least-squares problem of finding the field closest to the transported one that lies within bounds set by the neighboring elements' values, keeping the element's tracer mass.

Create the limiter once for a tracer density field (a scalar or a NamedTuple of tracers), and keep it in the model's cache:
```
limiter = Limiters.QuasiMonotoneLimiter(ρq)
```
Before the transport step, compute the bounds from the state the step starts from. In a multi-stage scheme, this is the stage's starting state:
```
Limiters.compute_bounds!(limiter, y.ρq, y.ρ)
```
After the step (or stage), apply the limiter to the transported tracer density, with the transported density as the weight:
```
Limiters.apply_limiter!(y_new.ρq, y_new.ρ, limiter)
```

On a distributed topology, compute_bounds! exchanges neighbor bounds across process boundaries. examples/plane/limiters_advection.jl, examples/sphere/limiters_advection.jl, and examples/hybrid/sphere/deformation_flow.jl run the standard advection tests with and without the limiter; the Example gallery states their equations.

Vertical mass borrowing limiter

Limiters.VerticalMassBorrowingLimiter(q_min) fills a negative tracer mass at one level by borrowing from the level below, and continues downward (and, if the bottom goes negative, back up) until every level satisfies the given minimum, conserving the column's tracer mass [15]:

limiter = Limiters.VerticalMassBorrowingLimiter((0.0, 0.0))  # one minimum per tracer
Limiters.apply_limiter!(q, ρ, limiter)

Limited vertical reconstructions

Vertical advection can be made monotone at the operator level rather than by a post-step limiter: Operators.LinVanLeerC2F (the van Leer limiter with the local-extrema constraint of [16]), Operators.TVDLimitedFluxC2F with a slope limiter (RZeroLimiter, MinModLimiter, KorenLimiter, SuperbeeLimiter, …), and the flux-corrected transport operators FCTBorisBook and FCTZalesak [17, 18] return limited face fluxes given the face velocity and the center field. Their docstrings on the finite-difference operators reference page give the stencils.