Environmental Engineering Reference
In-Depth Information
5.9 Coupled Time-Integration of Chemical
and Aerosol Dynamical Processes by Using
Multirate Implicit-Explicit Schemes
Ralf Wolke, Martin Schlegel, Elmar Filaus, Oswald Knoth,
and Eberhard Renner
Leibniz Institute for Tropospheric Research (IfT), Permoserstrasse 15, 04303 Leipzig,
Germany
Abstract
The application of suitable time integration schemes is especially important
for highly dynamical problems like atmospheric aerosol processes. Usually, classical
time integrators take the same time step over the complete domain and for all
components. Consequently, the model regions and the components with the strictest
time step restrictions dictate this global time step. Opposed to this, multirate schemes
are employed to adapt the time step locally, so that slower components take longer
and fewer time steps, which can reduce the computational costs substantially. In
the paper, a new class of time integration schemes is proposed which combines
the multirate approach with implicit-explicit (IMEX) methods. These schemes are
applied for block-structured grids with different horizontal resolutions as well as
the coupling between aerosol dynamical and gas phase chemical processes in the
chemistry-transport model COSMO-MUSCAT.
Keywords
Chemistry transport modeling, aerosol dynamics, time integration scheme,
multirate method
1. Introduction
In contrast to processes in the nature which perform in a coupled manner, these
are decoupled in numerical approaches using the “operator splitting” scheme. In
chemistry-transport models, such decoupling is often applied between the particular
transport processes (diffusion, advection in the different space directions), the
aerosol-dynamical transformations, the phase transfer and the chemical conversions
in gaseous and liquid phase. Then, the resulting splitting error can be kept small
only in the case of small time steps. For instance, changes in the aerosol population
or gas phase concentrations after a “long” transport time step can completely destroy
the thermodynamic balance in the grid cell, especially in regions with large dynamic
activity. Implicit-explicit (IMEX) schemes, which integrate the system in a coupled
