A Numerical Study of Methods for Moist Atmospheric Flows: Compressible Equations

Two common numerical techniques for integrating reversible moist processes in atmospheric flows are investigated in the context of solving the fully compressible Euler equations. The first is a one-step, coupled technique based on using appropriate invariant variables such that terms resulting from...

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Bibliographic Details
Published inMonthly weather review Vol. 142; no. 11; pp. 4269 - 4283
Main Authors Duarte, Max, Almgren, Ann S, Balakrishnan, Kaushik, Bell, John B, Romps, David M
Format Journal Article
LanguageEnglish
Published Washington American Meteorological Society 01.11.2014
Subjects
Acoustic insulation
Acoustics
Analysis of PDEs
Atmospheric flows
Clouds
Compressibility
Energy
Engineering Sciences
Euler-Lagrange equation
Fluid mechanics
Fluids mechanics
Gases
Heat
Mathematics
Mechanics
Meteorology
Numerical methods
Phase change
Physics
Saturation
Studies
Thermodynamics
Time
Transport equations
Variables
Water
Water vapor
Water vapour
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Summary:Two common numerical techniques for integrating reversible moist processes in atmospheric flows are investigated in the context of solving the fully compressible Euler equations. The first is a one-step, 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 two-step scheme, separate transport equations for liquid water and water vapor 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 Clausius-Clapeyron formula. The numerical techniques described are first validated by comparing to a well-established 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 two-step 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.
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ISSN:0027-0644
1520-0493
DOI:10.1175/MWR-D-13-00368.1