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  • 1
    Electronic Resource
    Electronic Resource
    A characteristic-Galerkin approximation to a system of shallow water equations (2000)
    Springer
    Numerische Mathematik 86 (2000), S. 239-256 
    Details
    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
    URL: http://dx.doi.org/10.1007/PL00005405
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A parallel, implicit, cell‐centered method for two‐phase flow with a preconditioned Newton–Krylov solver (1997)
    Springer
    Computational geosciences 1 (1997), S. 215-249 
    Details
    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
    URL: http://dx.doi.org/10.1023/A:1011521413158
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Modeling of in-situ biorestoration of organic compounds in groundwater (1991)
    Springer
    Transport in porous media 6 (1991), S. 667-702 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF00137855
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  • 4
    Electronic Resource
    Electronic Resource
    Godunov-mixed methods for immiscible displacement (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 835-847 
    Details
    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
    URL: http://dx.doi.org/10.1002/fld.1650110609
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Time-splitting for advection-dominated parabolic problems in one space variable (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 4 (1988), S. 413-423 
    Details
    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
    URL: http://dx.doi.org/10.1002/cnm.1630040316
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    Paper (German National Licenses)
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