  Convection schemes are a large source of error in global weather and climate
models, and modern resolutions are often too fine to parameterise convection
but are still too coarse to fully resolve it. Recently, numerical solutions of
multi-fluid equations have been proposed for a more flexible and consistent
treatment of sub-grid scale convection, including net mass transport by
convection and non-equilibrium dynamics. The technique involves splitting the
atmosphere into multiple fluids. For example, the atmosphere could be divided
into buoyant updrafts and stable regions. The fluids interact through a common
pressure, drag and mass transfers (entrainment and detrainment). Little is
known about the numerical properties of mass transfer terms between the fluids.
We derive mass transfer terms which relabel the fluids and derive numerical
properties of the transfer schemes, including boundedness, momentum
conservation and energy conservation. Numerical solutions of the multi-fluid
Euler equations using a C-grid are presented using stable and unstable
treatments of the transfers on a well-resolved two-fluid dry convection test
case. We find two schemes which are conservative, stable and bounded for large
timesteps, and maintain their numerical properties on staggered grids.
