A second-order Rosenbrock method applied to photochemical dispersion problems

• Published in: SIAM journal on scientific computing Vol. 20; no. 4; pp. 1456 - 1480
• Main Authors: VERWER, J. G, SPEE, E. J, BLOM, J. G, HUNDSDORFER, W
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 1999
• Subjects: Air pollution; Approximation theory; Atmospheric chemistry; Chemical reactions; Chemistry; Copyright; Exact sciences and technology; Mathematical models; Mathematical operators; Mathematics; Matrix algebra; Methods; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Outdoor air quality; Partial differential equations; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Photochemical reactions; Reaction kinetics; Sciences and techniques of general use; Sparsity; Second order equation; Transport equation; Numerical integration; Stability; Differential equation; Advection diffusion equation; Photochemical reaction; Reaction diffusion equation; Jacobi matrix; Strang operator; Rosenbrock methodRosenbrock method; Time dependence; Simulation; Box model; Air pollution; Stiff equation
• ISSN: 1064-8275; 1095-7197
• DOI: 10.1137/s1064827597326651

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 [PUBLICATION ABSTRACT]