Benchmarking stiff ode solvers for atmospheric chemistry problems II: Rosenbrock solvers

Abstract

In the numerical simulation of atmospheric transport-chemistry processes, a major task is the integration of the stiff systems of ordinary differential equations describing the chemical transformations. It is therefore of interest to systematically search for stiff solvers which can be identified as close to optimal for atmospheric applications. In this paper we continue our investigation from Sandu et al. (1996, CWI Report NM-R9603 and Report in Comput. Math., No. 85) and compare eight solvers on a set of seven box-models used in present day models. The focus is on Rosenbrock solvers. These tum out to be very well suited for our application when they are provided with highly efficient sparse matrix techniques to economize on the linear algebra. Two of the Rosenbrock solvers tested are from the literature, viz. RODAS and ROs4, and two are new and specially developed for air quality applications, viz. RODAS3 and ROS3. (f) 1997 Elsevier Science Ltd.

A computationally-efficient secondary organic aerosol module for three-dimensional air quality models

“…The maximum percentage deviations averaged over all time steps occur in the mixing ratios of HO 2 radical (i.e., 1.7% for the ROS3 solver and 2.5% for the QSSA solver) and the maximum percentage deviations at an instantaneous time step also occur for HO 2 radical (i.e., 4.2% for the ROS3 solver and 5.6% for the QSSA solver). These results are generally consistent with those of Sandu et al (1996Sandu et al ( , 1997aSandu et al ( , 1997b and Hesstvedt et al (1978). For all conditions, the QSSA solver is the fastest among the three solvers, while the ROS3 solver is slightly faster than the SMVGEAR solver for most simulations.…”

“…The use of such a box model isolates gaseous and aerosol chemical kinetics from other atmospheric processes such as emissions, transport, and depositions, on which the speedup is focused in this study. Three numerical solvers are implemented to solve CACM in the box model: the quasi steady state approximation solver (QSSA) (Hestveldt et al, 1978), the RosenBrock solver (ROS3) (Sandu et al, 1997a(Sandu et al, , 1997b, and the sparse-matrix vectorized Gear's solver (SMVGEAR) (Jacobson and Turco, 1994). The box model is set up for a one-day simulation starting 12:00 GMT (corresponds to 8 a.m. Eastern Daylight Time (EDT)), with a time step of 1 min for integration of gas-phase chemistry and aerosol processes.…”

Modelling the defrost process in complex geometries – part 2: wall-function based coupling to a multi-region CFD solver

“…The governing equations for the different stages during defrosting, together with the thermophysical properties, define a system of ordinary differential equations. This system with the respective boundary conditions at the two interfaces is solved using a solver based on the Rosenbrock method (rodas23 as described in [15]). The mesh and the fluid properties in the melting zone are adapted based on the displacement of the frost layer.…”

Transport and distribution of primary and secondary nonmethane volatile organic compounds in east Asia under continental outflow conditions

“…The numerical integration of the chemistry is done by a fully implicit integrator based on the Runge-KuttaRosenbrock type of solvers [Sandu et al, 1997].…”