E.J. Spee

A Second-Order Rosenbrock Method Applied to Photochemical Dispersion Problems

A second-order, L-stable Rosenbrock method from the field of stiff ordinary differential equations is studied for application to atmospheric dispersion problems describing photochemistry, advective, and turbulent diffusive transport. Partial differential equation problems of this type occur in the field of air pollution modeling. The focal point of the paper is to examine the Rosenbrock method for reliable and efficient use as an atmospheric chemical kinetics box-model solver within Strang-type operator splitting. In addition, two W-method versions of the Rosenbrock method are discussed. These versions use an inexact Jacobian matrix and are meant to provide alternatives for Strang-splitting. Another alternative for Strang-splitting is a technique based on so-called source-splitting. This technique is briefly discussed.

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 turn 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 Ros 4, and two are new and specially developed for air quality applications, viz. rodas 3 and ros 3.

A Comparison of Stiff ODE Solvers for Atmospheric Chemistry Problems

In the operator splitting solution of atmospheric transport-chemistry problems modeling air pollution, a major task is the numerical integration of the stiff systems of ordinary differential equations describing the chemical transformations. In this paper a numerical comparison is presented between two special purpose solvers developed for this task.