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  • Articles  (2)
  • Geosciences  (2)
  • 1
    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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  • 2
    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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    Paper (German National Licenses)
    Fulltext
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