Benchmarking stiff ode solvers for atmospheric chemistry problems-I. implicit vs explicit

Abstract

Abstract-In many applications of atmospheric transport-chemistry problems, a major task is the nwnerical integration of the stiff systems of ordinary differential equations describing the chemical transformations. This paper presents a comprehensive numerical comparison between five dedicated explicit and four implicit solvers for a set of seven benchmark problems from actual applications. The implicit solvers use sparse matrix techniques to economize on the numerical linear algebra overhead. As a result they are often more efficient than the dedicated explicit ones, particularly when approximately two or more figures of accuracy are required. In most test cases, sparse RODAS, a Rosenbrock solver, came out as most competitive in the 1 % error region. Of the dedicated explicit solvers, TWOSTEP came out as best. When less than 1 % accuracy is aimed at, this solver performs very efficiently for tropospheric gas-phase problems. However, like all other dedicated explicit solvers, it cannot efficiently deal with gas-liquid phase chemistry. The results presented may constitute a guide for atmospheric modelcrs to select a suitable integrator based on the type and dimension of their chemical mechanism and on the desired level of accuracy. Furthermore, we would like to consider this paper an open invitation for other groups to add new representative test problems to those described here and to benchmark their numerical algorithms in our standard computational environment.© 1997 Elsevier Science Ltd.

Tropospheric Ozone Assessment Report: Assessment of global-scale model performance for global and regional ozone distributions, variability, and trends

“…In addition to the uncertainty in reaction rate coefficients and absorption cross sections, and numerical uncertainties from the chemical solver code (e.g., Sandu et al, 1997), the main uncertainty in global chemical models comes from limitations in the representation of tropospheric chemistry. The computational expense of calculating chemical tendencies and tracer transport means that chemical mechanisms in global models are necessarily simplified, providing a relatively parsimonious description of gas phase tropospheric oxidation with respect to organic molecules and their oxidation pathways in particular (~50-250 species, ~5 00-1000 reactions) (e.g., Lamarque et al, 2013).…”

New insights into nocturnal nucleation

“…The Kinetic Pre-Processor (KPP; Sandu and Sanders, 2006) was used to translate the reaction equations into a Fortran 90 code that performs the time integration of the kinetic system. Of the several numerical solvers for systems of differential equations available in KPP, we used the LSODE solver (Radhakrishnan and Hindmarsh, 1993;Sandu et al, 1997). The KPP-produced FORTRAN code was then called from the main MALTE code.…”

Sensitivity Assessment of Ozone Models

“…The integration of chemical kinetics is computationally very expensive and can take more than 90'XOof the CPU runtime of an atmospheric chemical transport model peters et al, 1995;Sandilands and McConnel, 1997;and Sandu et al, 1997]. There are a number of methods for solving the kinetic equations in atmospheric models.…”

“…Integration of atmospheric chemical kinetics can take up to 90'%0of the total CPU time for current models. peters et al, 1995; Sandikmds and McConnel, 1997;and Sandu et al, 1997] Furthermore, it is becoming ever more apparent that heterogeneous, aqueous phase, and non-methane hydrocarbon chemistry is important for evaluation of emission impacts. ~arrison et al (1996); Ravishankara (1997); Finlayson-Pitts and Pitts (1997) Via these quantitative input-output relationships, a representation of the model can be used directly to calculate species concentrations and related chemical properties from inputs that characterize an initial photochemical state.…”