Eulerian Dispersion Models

Abstract

The main objectives of this chapter are to introduce the state-of-the-art numerical algorithms for the advection and diffusion used in Eulerian models and to discuss their theoretical and numerical characteristics. The Eulerian approach allows incorporation of different physical and chemical processes involved with the gaseous and particulate constituents in the atmosphere. The governing conservation equation for tracer species dispersion is derived. Approximations in the atmospheric dynamics and fundamental concepts used in the description of turbulence are explained. Some analytical solutions are provided for simplified dispersion conditions to illustrate basic processes in the atmospheric dispersion models. In the Eulerian approach, governing equations can be solved with a fractional time step or an explicit-implicit method to take advantage of numerical efficiency and knowledge of physical parameterizations of atmospheric surface flux exchange, advection, and diffusion processes. This chapter describes numerical solution methods for each physical process component in the Eulerian dispersion model. We provide fundamental steps used in the derivation of numerical advection algorithms, horizontal and vertical eddy diffusivity formulations, and local and non-local vertical diffusion methods. In the Appendix we have compiled vertical eddy diffusivity formulations in the literature, numerical solution methods of the local and non-local vertical diffusion algorithms, and Numerical algorithms with two-level time differencing for constant grid spacing.