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@ARTICLE{Dreger:1044264,
author = {Dreger, Raphael and Kirfel, Timo and Pozzer, Andrea and
Rosanka, Simon and Sander, Rolf and Taraborrelli, Domenico},
title = {{O}ptimized step size control within the {R}osenbrock
solvers for stiff chemical ordinary differential equation
systems in {KPP} version $2.2.3_rs4$},
journal = {Geoscientific model development},
volume = {18},
number = {13},
issn = {1991-959X},
address = {Katlenburg-Lindau},
publisher = {Copernicus},
reportid = {FZJ-2025-03134},
pages = {4273 - 4291},
year = {2025},
abstract = {Numerical integration of multiphase chemical kinetics in
atmospheric models is challenging. The underlying system of
ordinary differential equations (ODEs) is stiff and thus
difficult to solve. Rosenbrock solvers are a popular choice
for such tasks. These solvers provide the desired stability
and accuracy of results at an affordable yet large
computational cost. The latter is crucially dependent on the
efficiency of the step size control. Our analysis indicates
that the local error, which is the key factor for the step
size selection, is often overestimated, leading to very
small substeps. In this study, we optimized the first-order
step size controller most commonly employed in Rosenbrock
solvers. Furthermore, we compared its efficiency to a
second-order step size controller. We assessed the
performance of the controllers in both a box and a global
model for very stiff ODEs. Significant reductions in the
computation time were accomplished with only marginal
deviations in the results compared to the standard
first-order controller. This was achieved not only for
gas-phase chemistry but also for the more complex
aqueous-phase chemistry in cloud droplets and deliquescent
aerosols. Depending on the selected chemical mechanism,
significant improvements were already achieved by simply
adjusting heuristic parameters of the default controller.
However, especially for the global model, the best results
were achieved with the second-order controller, which
reduced the number of function evaluations by $43 \%,$
$27 \%$ and $13 \%$ for gas-phase, cloud and aerosol
chemistry, respectively. The overall computational time was
reduced by over $11 \%$ while requiring only minimal
adjustments to the original code. Analysis of a 1-year
integration period showed that with the second-order
controller, the deviations from the reference simulation
stay below $1 \%$ for the main tropospheric oxidants. The
results presented here show the possibility of more
efficient atmospheric chemistry simulations without
compromising accuracy.},
cin = {ICE-3},
ddc = {550},
cid = {I:(DE-Juel1)ICE-3-20101013},
pnm = {2111 - Air Quality (POF4-211)},
pid = {G:(DE-HGF)POF4-2111},
typ = {PUB:(DE-HGF)16},
UT = {WOS:001528724000001},
doi = {10.5194/gmd-18-4273-2025},
url = {https://juser.fz-juelich.de/record/1044264},
}