Passive Scalars

The scalars package advects passive scalar fields with the flow. Scalars are one-way coupled: they are transported by the hydrodynamic velocity but do not feed back on the dynamics. They are typically used as tracers, tagging a region or material with a value of one and zero elsewhere. Any number of scalars may be defined. The package requires hydrodynamics to be enabled.

Governing Equations

RIOT supports two kinds of passive scalar.

Material-Tied Scalars

A material-tied scalar is a mass fraction \(c\) carried by a particular material. Its conserved density \(C = \bar\rho_m\,c\) is advected in flux-conservation form with no source,

\[\frac{\partial \left(\bar\rho_m c\right)}{\partial t} + \nabla\!\cdot\!\left(\bar\rho_m c\,\vec{v}\right) = 0 ,\]

and the primitive mass fraction is recovered as \(c = C/\bar\rho_m\). Because it is tied to a material, the scalar is a sparse field that is allocated and deallocated together with that material.

Bulk-Tied Scalars

A bulk-tied scalar \(\psi\) is not associated with any mass; it is a dense field advected directly with the bulk velocity,

\[\frac{\partial \psi}{\partial t} + \nabla\!\cdot\!\left(\psi\,\vec{v}\right) = 0 .\]

No primitive/conserved distinction is required for a bulk-tied scalar.

Both kinds are advected with the same reconstruction and Riemann machinery as the hydrodynamic fields (Chapter Hydrodynamics).

Input Parameters

Passive scalars are enabled with the scalars toggle in the <physics> block (Section Enabling Physics: the <physics> Block); hydro must also be enabled. Each scalar is defined in a contiguous, zero-based block <scalars0>, <scalars1>, …. Whether a scalar is material-tied or bulk-tied is determined by the presence of the matid parameter.

Per-scalar parameters in each `<scalars`\(N\)`>` block.
Parameter	Type	Default	Description
label	string	block	Name of the scalar field (defaults to the block name).
matid	int	—	Material ID to tie the scalar to; if omitted, the scalar is bulk-tied.

Registered Fields

For each material-tied scalar the package registers a conserved (advected) field and its derived primitive counterpart; a bulk-tied scalar registers a single advected field. The exact field names are taken from the user’s label; the table below shows their structure.

Fields registered per scalar (names taken from `label`).
Field	Symbol	Components	Metadata / description
label (material-tied)	\(\bar\rho_m c\)	1	Cell, Independent, Intensive, Sparse, FillGhost, Advected, WithFluxes; conserved scalar density.
prim.label	\(c\)	1	Cell, Sparse, Derived, OneCopy; primitive mass fraction.
label (bulk-tied)	\(\psi\)	1	Cell, Independent, Intensive, FillGhost, Advected, WithFluxes; bulk-advected scalar.

Example

One material-tied tracer on material 0 and one bulk-tied tracer:

riot.input("physics", hydro=True, scalars=True)
riot.input("scalars0", label="dye", matid=0)  # tied to material 0
riot.input("scalars1", label="marker")        # no matid => bulk-tied