A Numerical Study of Methods for Moist Atmospheric Flows: Compressible Equations
Abstract
We investigate two common numerical techniques for integrating reversible moist processes in atmospheric flows in the context of solving the fully compressible Euler equations. The first is a onestep, coupled technique based on using appropriate invariant variables such that terms resulting from phase change are eliminated in the governing equations. In the second approach, which is a twostep scheme, separate transport equations for liquid water and vapor water are used, and no conversion between water vapor and liquid water is allowed in the first step, while in the second step a saturation adjustment procedure is performed that correctly allocates the water into its two phases based on the ClausiusClapeyron formula. The numerical techniques we describe are first validated by comparing to a wellestablished benchmark problem. Particular attention is then paid to the effect of changing the time scale at which the moist variables are adjusted to the saturation requirements in two different variations of the twostep scheme. This study is motivated by the fact that when acoustic modes are integrated separately in time (neglecting phase change related phenomena), or when soundproof equations are integrated, the time scale for imposing saturation adjustment is typically much larger than the numerical one related to the acoustics.
 Publication:

Monthly Weather Review
 Pub Date:
 November 2014
 DOI:
 10.1175/MWRD1300368.1
 arXiv:
 arXiv:1311.4265
 Bibcode:
 2014MWRv..142.4269D
 Keywords:

 Physics  Atmospheric and Oceanic Physics;
 Mathematics  Analysis of PDEs;
 Physics  Fluid Dynamics
 EPrint:
 Monthly Weather Review 142 (11), 42694283 (2014)