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- Title
Numerical methods for entrainment and detrainment in the multi‐fluid Euler equations for convection.
- Authors
McIntyre, William A.; Weller, Hilary; Holloway, Christopher E.
- Abstract
Convection schemes are a large source of error in global weather and climate models, and modern resolutions are often too fine to parametrize 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 subgrid‐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 updraughts 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 on a co‐located grid. Numerical simulations 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 time steps, and maintain their numerical properties on staggered grids.
- Subjects
TRANSPORT equation; NUMERICAL solutions to equations; MASS transfer; ENERGY conservation; ATMOSPHERIC models; EULER equations; NATURAL heat convection; WATER masses
- Publication
Quarterly Journal of the Royal Meteorological Society, 2020, Vol 146, Issue 728, p1106
- ISSN
0035-9009
- Publication type
Article
- DOI
10.1002/qj.3728