Numerical simulation of water resources problems: Models, methods, and trends
Mechanistic modeling of water resources systems is a broad field with abundant challenges. We consider classes of model formulations that are considered routine, the focus of current work, and the foundation of foreseeable work over the coming decade. These model formulations are used to assess the current and evolving state of solution algorithms, discretization methods, nonlinear and linear algebraic solution methods, computational environments, and hardware trends and implications. The goal of this work is to provide guidance to enable modelers of water resources systems to make sensible choices when developing solution methods based upon the current state of knowledge and to focus future collaborative work among water resources scientists, applied mathematicians, and computational scientists on productive areas.
© 2012 Elsevier Ltd. Available online 31 May 2012. The work of CTM was supported by Department of Energy Grant DE-SC0002163 and National Science Foundation Grant CDI-0941235. The work of CND was supported by National Science Foundation Grant DMS 0915223. The work of MWF and CEK was supported by the Civil Works and Military Engineering 6.1 research programs of the U.S. Army Corps of Engineers and the Coastal and Hydraulics Laboratory Internal Research Investment Program. Permission was granted by the Chief of Engineers to publish this information. The work of TYH was supported by AFOSR MURI Grant FA9550–09-1–0613, Department of Energy Grant DE-FG02–06ER25727, and National Science Foundation Grant DMS-0908546. The work of JH was supported by NSF Grants DMS-0811130 and CDI-0941235. The work of CTK was supported by ARO Grant W911NF-11–1-0367, US Army Corps of Engineers Contract W912HZ-11-P-0385, and NSF Grant CDI-0941253. The work of HPL was supported by a Center of Excellence grant from the Research Council of Norway to the Center for Biomedical Computing at Simula Research Laboratory.