FluxVariables is a misnomer

The classes [...]FluxVariables actually computes fluxes for which it uses variables from the VolumeVariables and FluxVariablesCache. It does store local variable objects in its state but the main interface is all about computing fluxes. Also, they are used directly within LocalResidal::computeFlux as a helper to compute fluxes (evaluate the flux-part of the local residual).

Possible better names would be [...]Flux [...]Fluxes.