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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 86 (2000), S. 239-256 
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. Characteristic methods are known to handle advective flow better than traditional Galerkin methods and allow large time steps to be taken when compared to standard time-stepping methods. In this paper, we investigate a characteristic-Galerkin approximation to the 2-dimensional system of shallow water equations. We derive ${\cal L}^{\infty}\left ((0,T);{\cal L}^2(\Omega)\right )$ bounds for elevation and velocity, showing these to be optimal for velocity in ${\cal L}^2\left ((0,T);{\cal H}^1(\Omega)\right )$ .
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1573-1499
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Computer Science
    Notes: Abstract A new parallel solution technique is developed for the fully implicit three‐dimensional two‐phase flow model. An expandedcell‐centered finite difference scheme which allows for a full permeability tensor is employed for the spatial discretization, and backwardEuler is used for the time discretization. The discrete systems are solved using a novel inexact Newton method that reuses the Krylov information generated by the GMRES linear iterative solver. Fast nonlinear convergence can be achieved by composing inexact Newton steps with quasi‐Newton steps restricted to the underlying Krylov subspace. Furthermore, robustness and efficiency are achieved with a line‐search backtracking globalization strategy for the nonlinear systems and a preconditioner for each coupled linear system to be solved. This inexact Newton method also makes use of forcing terms suggested by Eisenstat and Walker which prevent oversolving of the Jacobian systems. The preconditioner is a new two‐stage method which involves a decoupling strategy plus the separate solutions of both nonwetting‐phase pressure and saturation equations. Numerical results show that these nonlinear and linear solvers are very effective.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Transport in porous media 6 (1991), S. 667-702 
    ISSN: 1573-1634
    Keywords: Modified method of characteristics ; time-splitting ; in situ biorestoration ; adsorption ; contaminant transport
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract A convergent numerical method for modeling in situ biorestoration of contaminated groundwater is outlined. This method treats systems of transport-biodegradation equations by operator splitting in time. Transport is approximated by a finite element modified method of characteristics. The biodegradation terms are split from the transport terms and treated as a system of ordinary differential equations. Numerical results for vertical cross-sectional flow are presented. The effects of variable hydraulic conductivity and variable linear adsorption are studied.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 835-847 
    ISSN: 0271-2091
    Keywords: Higher-order Godunov method ; Mixed finite element method ; Immiscible displacement ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The immiscible displacement problem in reservoir engineering can be formulated as a system of partial differential equations which includes an elliptic pressure-velocity equation and a degenerate parabolic saturation equation. We apply a sequential numerical scheme to this problem where time splitting is used to solve the saturation equation. In this procedure one approximates advection by a higher-order Godunov method and diffusion by a mixed finite element method. Numerical results for this scheme applied to gas-oil centrifuge experiments are given.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 4 (1988), S. 413-423 
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Publication Date: 2022-05-25
    Description: Author Posting. © The Oceanography Society, 2016. This article is posted here by permission of The Oceanography Society for personal use, not for redistribution. The definitive version was published in Oceanography 29, no. 3 (2016): 96–107, doi:10.5670/oceanog.2016.74.
    Description: The 2010 Deepwater Horizon (DWH) oil spill in the Gulf of Mexico resulted in the collection of a vast amount of situ and remotely sensed data that can be used to determine the spatiotemporal extent of the oil spill and test advances in oil spill models, verifying their utility for future operational use. This article summarizes observations of hydrocarbon dispersion collected at the surface and at depth and our current understanding of the factors that affect the dispersion, as well as our improved ability to model and predict oil and gas transport. As a direct result of studying the area where oil and gas spread during the DWH oil spill, our forecasting capabilities have been greatly enhanced. State-of-the-art oil spill models now include the ability to simulate the rise of a buoyant plume of oil from sources at the seabed to the surface. A number of efforts have focused on improving our understanding of the influences of the near-surface oceanic layer and the atmospheric boundary layer on oil spill dispersion, including the effects of waves. In the future, oil spill modeling routines will likely be included in Earth system modeling environments, which will link physical models (hydrodynamic, surface wave, and atmospheric) with marine sediment and biogeochemical components.
    Description: This research was made possible by a grant from BP/The Gulf of Mexico Research Initiative to the CARTHE and Deep-C Consortia, and by contract M12PC00003 from the Bureau of Ocean Energy Management (BOEM).
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 7
    Publication Date: 2022-05-25
    Description: © The Author(s), 2019. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Fringer, O. B., Dawson, C. N., He, R., Ralston, D. K., & Zhang, Y. J. The future of coastal and estuarine modeling: findings from a workshop. Ocean Modelling, 143, (2019): 101458, doi:10.1016/j.ocemod.2019.101458.
    Description: This paper summarizes the findings of a workshop convened in the United States in 2018 to discuss methods in coastal and estuarine modeling and to propose key areas of research and development needed to improve their accuracy and reliability. The focus of this paper is on physical processes, and we provide an overview of the current state-of-the-art based on presentations and discussions at the meeting, which revolved around the four primary themes of parameterizations, numerical methods, in-situ and remote-sensing measurements, and high-performance computing. A primary outcome of the workshop was agreement on the need to reduce subjectivity and improve reproducibility in modeling of physical processes in the coastal ocean. Reduction of subjectivity can be accomplished through development of standards for benchmarks, grid generation, and validation, and reproducibility can be improved through development of standards for input/output, coupling and model nesting, and reporting. Subjectivity can also be reduced through more engagement with the applied mathematics and computer science communities to develop methods for robust parameter estimation and uncertainty quantification. Such engagement could be encouraged through more collaboration between the forward and inverse modeling communities and integration of more applied math and computer science into oceanography curricula. Another outcome of the workshop was agreement on the need to develop high-resolution models that scale on advanced HPC systems to resolve, rather than parameterize, processes with horizontal scales that range between the depth and the internal Rossby deformation scale. Unsurprisingly, more research is needed on parameterizations of processes at scales smaller than the depth, including parameterizations for drag (including bottom roughness, bedforms, vegetation and corals), wave breaking, and air–sea interactions under strong wind conditions. Other topics that require significantly more work to better parameterize include nearshore wave modeling, sediment transport modeling, and morphodynamics. Finally, it was agreed that coastal models should be considered as key infrastructure needed to support research, just like laboratory facilities, field instrumentation, and research vessels. This will require a shift in the way proposals related to coastal ocean modeling are reviewed and funded.
    Description: We thank Carmen Torres at Stanford University and Jennifer Warrillow at North Carolina State University for their assistance with workshop logistics. Helpful comments and suggestions were provided by two anonymous reviewers and Hans Burchard and John Warner. The workshop and preparation of this paper were funded by U.S. National Science Foundation Grant OCE-1749613.
    Keywords: Coastal ocean modeling ; Physical processes ; Model subjectivity ; Development of standards ; High-resolution modeling ; Parameter estimation
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 8
    Publication Date: 2022-05-27
    Description: Author Posting. © American Meteorological Society, 2021. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Bulletin of the American Meteorological Society 102(1), (2021): E99-E122, https://doi.org/10.1175/BAMS-D-19-0005.1.
    Description: The Red Sea, home to the second-longest coral reef system in the world, is a vital resource for the Kingdom of Saudi Arabia. The Red Sea provides 90% of the Kingdom’s potable water by desalinization, supporting tourism, shipping, aquaculture, and fishing industries, which together contribute about 10%–20% of the country’s GDP. All these activities, and those elsewhere in the Red Sea region, critically depend on oceanic and atmospheric conditions. At a time of mega-development projects along the Red Sea coast, and global warming, authorities are working on optimizing the harnessing of environmental resources, including renewable energy and rainwater harvesting. All these require high-resolution weather and climate information. Toward this end, we have undertaken a multipronged research and development activity in which we are developing an integrated data-driven regional coupled modeling system. The telescopically nested components include 5-km- to 600-m-resolution atmospheric models to address weather and climate challenges, 4-km- to 50-m-resolution ocean models with regional and coastal configurations to simulate and predict the general and mesoscale circulation, 4-km- to 100-m-resolution ecosystem models to simulate the biogeochemistry, and 1-km- to 50-m-resolution wave models. In addition, a complementary probabilistic transport modeling system predicts dispersion of contaminant plumes, oil spill, and marine ecosystem connectivity. Advanced ensemble data assimilation capabilities have also been implemented for accurate forecasting. Resulting achievements include significant advancement in our understanding of the regional circulation and its connection to the global climate, development, and validation of long-term Red Sea regional atmospheric–oceanic–wave reanalyses and forecasting capacities. These products are being extensively used by academia, government, and industry in various weather and marine studies and operations, environmental policies, renewable energy applications, impact assessment, flood forecasting, and more.
    Description: The development of the Red Sea modeling system is being supported by the Virtual Red Sea Initiative and the Competitive Research Grants (CRG) program from the Office of Sponsored Research at KAUST, Saudi Aramco Company through the Saudi ARAMCO Marine Environmental Center at KAUST, and by funds from KAEC, NEOM, and RSP through Beacon Development Company at KAUST.
    Repository Name: Woods Hole Open Access Server
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  • 9
    Publication Date: 2000-08-01
    Print ISSN: 0029-599X
    Electronic ISSN: 0945-3245
    Topics: Mathematics
    Published by Springer
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  • 10
    Publication Date: 2019-11-01
    Print ISSN: 1463-5003
    Electronic ISSN: 1463-5011
    Topics: Geography , Geosciences , Physics
    Published by Elsevier
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