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Numerical simulation of water resources problems: Models, methods, and trends

Miller, Cass T. and Dawson, Clint N. and Farthing, Matthew W. and Hou, Thomas Y. and Huang, Jingfang and Kees, Christopher E. and Kelley, C. T. and Langtangen, Hans Petter (2013) Numerical simulation of water resources problems: Models, methods, and trends. Advances in Water Resources, 51 . pp. 405-437. ISSN 0309-1708.

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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.

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Additional Information:© 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.
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0002163
NSFDMS 0915223
U.S. Army Corps of EngineersUNSPECIFIED
Coastal and Hydraulics Laboratory Internal Research Investment ProgramUNSPECIFIED
Air Force Office of Scientific Research (AFOSR) Multidisciplinary University Research Initiative (MURI)FA9550–09-1–0613
Department of Energy (DOE)DE-FG02–06ER25727
Army Research Office (ARO)W911NF-11–1-0367
U.S. Army Corps of Engineers ContractW912HZ-11-P-0385
Research Council of Norway Center of Excellence grantUNSPECIFIED
Subject Keywords:Adaptive methods; Problem solving environments; Multiscale methods; Integral methods; GPUs; Error estimation and control
Record Number:CaltechAUTHORS:20130305-095227632
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Official Citation:Cass T. Miller, Clint N. Dawson, Matthew W. Farthing, Thomas Y. Hou, Jingfang Huang, Christopher E. Kees, C.T. Kelley, Hans Petter Langtangen, Numerical simulation of water resources problems: Models, methods, and trends, Advances in Water Resources, Volume 51, January 2013, Pages 405-437, ISSN 0309-1708, 10.1016/j.advwatres.2012.05.008. (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37298
Deposited By: Ruth Sustaita
Deposited On:05 Mar 2013 18:50
Last Modified:03 Oct 2019 04:46

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