The atmosphere is a challenging fluid to simulate numerically. Unlike liquids, air is compressible: its density varies by an order of magnitude throughout the troposphere. In addition, atmospheric air is moist: it contains water in all three phases, and transitions between those phases release and absorb heat. Furthermore, the air density and water phases interact with each other: changes in density affect the phase changes of water, and the phase changes of water affect the density.
When simulating a compressible flow with phase changes, decisions must be made about how to handle the compressibility and the phase changes. For computational speed, these are integrated on different time scales, with the compressibility handled on a much shorter timescale than the phase changes. This approach can lead to errors, however, if the separation in timescales is too large. This study explores different methods for simulating moist convection, with special attention paid to these errors.
Temperature (2-K contours) for a moist bubble in two dimensions integrated numerically in four different ways. The black contours show the benchmark simulation. The red contours show the results obtained with different time steps for updating the phase transitions, with a maximum time step of 30 seconds in the lower-right panel.