Summary: The main goal of this article is to review problems arising from important issues related to energy and environment, and computational methods to address them quantitatively. The article consists of two parts, which have a lot in common, the modeling and simulation of the physico-chemistry phenomena associated with air pollution and quality, and a similar approach to investigate energy related issues, focusing mostly on oil and gas production. In both cases the phenomena under consideration are modeled by partial differential equations of advection-reaction-diffusion type. We describe and comment on these models and discuss solution methods for the related partial differential equations. These methods include finite difference, finite element and finite volume space approximations, and splitting and non-splitting time discretizations. The results of test problems solved by such methods are presented and validated by comparisons with experimental data and output from other computational methods.
For the entire collection see [Zbl 1024.00037].