| Abstract: |
| This talk concerns the mathematical analysis of a cloud resolving model which includes the ice microphysics. The main system is coupling the potential temperature \theta, the water vapor mixing ratio q_v, the cloud condensate mixing ratio q_c, and the precipitation water mixing ratio q_p. The evolution of these quantities includes the terms involving the condensate from water vapor (CON), auto-conversion of cloud condensate (AUT), and accretion of cloud condensate by precipitation (ACC), and the source of precipitation due to deposition of water vapor on precipitation particles (DEP). The physical modeling of these quantities is first briefly recalled.
The most important mathematical difficulty of this complex system is to deal with the constraint q_v \le q_vs so the solution is subjected to belonging to a convex set, which in turn depends on the solution, hence the mathematical modeling by a quasi-variational inequality, a concept first introduced by Bensoussan and Lions. The paper proceeds by proving a priori estimates for the penalized solution involving a penalization parameter \epsilon. The solution is then obtained by passing to the limit \epsilon going to 0. If time permits, some numerical simulations will be displayed involving geographic obstacles containing two mountains. The simulations show agreement with physics thus showing the physical soundness of the system. |
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